A comparison of different choices of clocks in a reduced phase space quantization in loop quantum cosmology with an inflationary potential using effective techniques - Giesel, Kristina; Li, Bao-Fei; Singh, Parampreet (The Sixteenth Marcel Grossmann Meeting, pp. 4228-4233 (2023), 2023)
We review recent results that apply a reduced phase space quantization of loop quantum cosmology (LQC) for a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe filled with reference fields and an inflaton field in a Starobinsky inflationary potential. All three models that we consider are two-fluid models and they differ by their choice of global clock which are chosen to be either Gaussian dust, Brown-Kuchař dust or a massless Klein-Gordon scalar field. Although two-fluid models are more complicated than models involving the inflaton only, it turns out that some of the technical hurdles in conventional quantum cosmological models can be bypassed in these models. Using the effective dynamics resulting from the reduced phase space quantization we discuss some phenomenological implications of these models including the resolution of the big bang singularity via a quantum bounce and in addition address the question whether different choices of clocks can leave an imprint on the inflationary dynamics.<br

A gravitationally induced decoherence model using Ashtekar variables - Fahn, Max Joseph; Giesel, Kristina; Kobler, Michael (Classical and Quantum Gravity, 2023)
We consider the coupling of a scalar field to linearised gravity and derive a relativistic gravitationally induced decoherence model using Ashtekar variables. The model is formulated at the gauge invariant level using suitable geometrical clocks in the relational formalism, broadening existing gauge invariant formulations of decoherence models. For the construction of the Dirac observables we extend the known observable map by a kind of dual map where the role of clocks and constraints is interchanged. We also discuss a second choice of geometrical clocks existing in the ADM literature. Then we apply a reduced phase space quantisation on Fock space and derive the final master equation choosing a Gibbs state for the gravitational environment and using the projection operator technique. The resulting master equation is not automatically of Lindblad type, a starting point sometimes assumed for phenomenological models, but still involves a residual time dependence at the level of the effective operators in the master equation due to the form of the correlation functions that we express in terms of thermal Wightman functions. Furthermore, we discuss why in the model analysed here the application of a second Markov approximation in order to obtain a set of time independent effective system operators is less straightforward than in some of the quantum mechanical models.
CRIS-Team Scopus Importer:2023-04-28
Keywords: decoherence; Dirac observables; geometrical clocks; linearised gravity; master equation

Algebraic Loop Quantisation of the Gowdy Model: The Master Constraint - Alex, Nils; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2015)

Algebraic quantum gravity (AQG): I. Conceptual setup - Giesel, Kristina; Thiemann, Thomas (Classical and Quantum Gravity, 2007)
We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single master constraint operator. While AQG is inspired by loop quantum gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of general relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken. There simply is no lattice regulator that must be sent to zero.

Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory - Giesel, Kristina; Thiemann, Thomas (Classical and Quantum Gravity, 2007)
In the two previous papers of this series we defined a new combinatorial approach to quantum gravity, algebraic quantum gravity (AQG). We showed that AQG reproduces the correct infinitesimal dynamics in the semiclassical limit, provided one incorrectly substitutes the non-Abelian group SU(2) by the Abelian group U(1)(3) in the calculations. The mere reason why that substitution was performed at all is that in the non-Abelian case the volume operator, pivotal for the definition of the dynamics, is not diagonizable by analytical methods. This, in contrast to the Abelian case, so far prohibited semiclassical computations. In this paper, we show why this unjustified substitution nevertheless reproduces the correct physical result. Namely, we introduce for the first time semiclassical perturbation theory within AQG ( and LQG) which allows us to compute expectation values of interesting operators such as the master constraint as a power series in h with error control. That is, in particular, matrix elements of fractional powers of the volume operator can be computed with extremely high precision for sufficiently large power of h in the h expansion. With this new tool, the non-Abelian calculation, although technically more involved, is then exactly analogous to the Abelian calculation, thus justifying the Abelian analysis in retrospect. The results of this paper turn AQG into a calculational discipline.

Algebraic quantum gravity (AQG): II. Semiclassical analysis - Giesel, Kristina; Thiemann, Thomas (Classical and Quantum Gravity, 2007)
In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity (AQG), was introduced. In the framework of AQG, existing semiclassical tools can be applied to operators that encode the dynamics of AQG such as the master constraint operator. In this paper, we will analyse the semiclassical limit of the (extended) algebraic master constraint operator and show that it reproduces the correct infinitesimal generators of general relativity. Therefore, the question of whether general relativity is included in the semiclassical sector of the theory, which is still an open problem in LQG, can be significantly improved in the framework of AQG. For the calculations, we will substitute SU(2) with U(1)(3). That this substitution is justified will be demonstrated in the third paper ( Giesel and Thiemann 2006 Semiclassical perturbation theory Preprint gr-qc/0607101) of this series.

Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity - Giesel, Kristina; Thiemann, Thomas (Classical and Quantum Gravity, 2010)
We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of (a) the Brown-Kuchar mechanism in the presence of pressure-free dust fields which allows to deparametrize the theory and (b) Rovelli's relational formalism in the extended version developed by Dittrich to construct the algebra of gauge-invariant observables. Since the resulting algebra of observables is very simple, one can quantize it using the methods of LQG. Basically, the kinematical Hilbert space of non-reduced LQG now becomes a physical Hilbert space and the kinematical results of LQG such as discreteness of spectra of geometrical operators now have physical meaning. The constraints have disappeared; however, the dynamics of the observables is driven by a physical Hamiltonian which is related to the Hamiltonian of the standard model (without dust) and which we quantize in this paper.

Analysing (cosmological) singularity avoidance in loop quantum gravity using U (1)(3) coherent states and Kummer's functions - Giesel, Kristina; Winnekens, David (Classical and Quantum Gravity, 2023)
Using a new procedure based on Kummer's Confluent Hypergeometric Functions, we investigate the question of singularity avoidance in loop quantum gravity (LQG) in the context of U(1)(3) complexifier coherent states and compare obtained results with already existing ones. Our analysis focuses on the dynamical operators, denoted by (q) over cap (i0)(I0) (r), whose products are the analogue of the inverse scale factor in LQG and also play a pivotal role for other dynamical operators such as matter Hamiltonians or the Hamiltonian constraint. For graphs of cubic topology and linear powers in (q) over cap (i0)(I0) (r), we obtain the correct classical limit and demonstrate how higher order corrections can be computed with this method. This extends already existing techniques in the way how the involved fractional powers are handled. We also extend already existing formalisms to graphs with higher-valent vertices. For generic graphs and products of (q) over cap (i0)(I0) (r), using estimates becomes inevitable and we investigate upper bounds for these semiclassical expectation values. Compared to existing results, our method allows to keep fractional powers involved in (q) over cap (i0)(I0) (r) throughout the computations, which have been estimated by integer powers elsewhere. Similar to former results, we find a non-zero upper bound for the inverse scale factor at the initial singularity. Additionally, our findings provide some insights into properties and related implications of the results that arise when using estimates and can be used to look for improved estimates.
CRIS-Team WoS Importer:2023-04-21

An Open Scattering Model in Polymerized Quantum Mechanics - Giesel, Kristina; Kobler, Michael (Mathematics, 2022)
We derive a quantum master equation in the context of a polymerized open quantum mechanical system for the scattering of a Brownian particle in an ideal gas environment. The model is formulated in a top-down approach by choosing a Hamiltonian with a coupling between the system and environment that is generally associated with spatial decoherence. We extend the existing work on such models by using a non-standard representation of the canonical commutation relations, inspired by the quantization procedure applied in loop quantum gravity, which yields a model in which position operators are replaced by holonomies. The derivation of the master equation in a top-down approach opens up the possibility to investigate in detail whether the assumptions, usually used in such models in order to obtain a tractable form of the dissipator, hold also in the polymerized case or whether they need to be dropped or modified. Furthermore, we discuss some physical properties of the master equation associated to effective equations for the expectation values of the fundamental operators and compare our results to the already existing models of collisional decoherence.
CRIS-Team Scopus Importer:2022-12-02
Keywords: decoherence models; open quantum systems; polymer quantum mechanics

Coherent states for fractional powers of the harmonic oscillator Hamiltonian - Giesel, Kristina; Vetter, Almut (Universe, 2021)
Inspired by special and general relativistic systems that can have Hamiltonians involving square roots or more general fractional powers, in this article, we address the question of how a suitable set of coherent states for such systems can be obtained. This becomes a relevant topic if the semiclassical sector of a given quantum theory is to be analysed. As a simple setup, we consider the toy model of a deparametrised system with one constraint that involves a fractional power of the harmonic oscillator Hamiltonian operator, and we discuss two approaches to finding suitable coherent states for this system. In the first approach, we consider Dirac quantisation and group averaging, as have been used by Ashtekar et al., but only for integer powers of operators. Our generalisation to fractional powers yields in the case of the toy model a suitable set of coherent states. The second approach is inspired by coherent states based on a fractional Poisson distribution introduced by Laskin, which however turn out not to satisfy all properties to yield good semiclassical results for the operators considered here and in particular do not satisfy a resolution of identity as claimed. Therefore, we present a generalisation of the standard harmonic oscillator coherent states to states involving fractional labels, which approximate the fractional operators in our toy model semiclassically more accurately and satisfy a resolution of identity. In addition, motivated by the way the proof of the resolution of identity is performed, we consider these kind of coherent states also for the polymerised harmonic oscillator and discuss their semiclassical properties.
Keywords: coherent states; constrained systems; operators involving fractional powers; semiclassical analysis

Coherent states on the circle: semiclassical matrix elements in the context of Kummer functions and the Zak transformation - Giesel, Kristina; Winnekens, David (Physica Scripta, 2023)
We extend former results for coherent states on the circle in the literature in two ways. On the one hand, we show that expectation values of fractional powers of momentum operators can be computed exactly analytically by means of Kummer’s confluent hypergeometric functions. Earlier, these expectation values have only been obtained by using suitable estimates. On the other hand, we consider the Zak transformation not only to map harmonic oscillator coherent states to coherent states on the circle as it has been discussed before, but we also use the properties of the Zak transformation to derive a relation between matrix elements with respect to coherent states in L 2 ( R ) and L 2(S 1). This provides an alternative way for computing semiclassical matrix elements for coherent states on the circle. In certain aspects, this method simplifies the semiclassical computations in particular if one is only interested in the classical limit, that is the zeroth order term in the semiclassical expansion.
CRIS-Team Scopus Importer:2023-08-25
Keywords: coherent states; Kummer functions; semiclassical analysis; Zak transformation

Comparison Between Dirac and Reduced Quantization in LQG-Models with Klein-Gordon Scalar Fields - Giesel, Kristina; Oelmann, Almut (Acta Physica Polonica B, 2017)

Consistency check on volume and triad operator quantization in loop quantum gravity: I - Giesel, Kristina; Thiemann, Thomas (Classical and Quantum Gravity, 2006)
The volume operator plays a pivotal role for the quantum dynamics of loop quantum gravity (LQG). It is essential to construct triad operators that enter the Hamiltonian constraint and which become densely defined operators on the full Hilbert space, even though in the classical theory the triad becomes singular when classical GR breaks down. The expression for the volume and triad operators derives from the quantization of the fundamental electric flux operator of LQG by a complicated regularization procedure. In fact, there are two inequivalent volume operators available in the literature and, moreover, both operators are unique only up to a finite, multiplicative constant which should be viewed as a regularization ambiguity. Now on the one hand, classical volumes and triads can be expressed directly in terms of fluxes and this fact was used to construct the corresponding volume and triad operators. On the other hand, fluxes can be expressed in terms of triads and triads can be replaced by Poisson brackets between the holonomy and the volume operators. Therefore one can also view the holonomy operators and the volume operator as fundamental and consider the flux operator as a derived operator. In this paper we mathematically implement this second point of view and thus can examine whether the volume, triad and flux quantizations are consistent with each other. The results of this consistency analysis are rather surprising. Among other findings we show the following. ( 1) The regularization constant can be uniquely fixed. ( 2) One of the volume operators can be ruled out as inconsistent. ( 3) Factor ordering ambiguities in the definition of triad operators are immaterial for the classical limit of the derived flux operator. The results of this paper show that within full LQG triad operators are consistently quantized.

Consistency check on volume and triad operator quantization in loop quantum gravity: II - Giesel, Kristina; Thiemann, Thomas (Classical and Quantum Gravity, 2006)
In this paper, we provide the techniques and proofs for the results presented in our companion paper concerning the consistency check on volume and triad operator quantization in loop quantum gravity.

Consistent gauge-fixing conditions in polymerized gravitational systems - Giesel, Kristina; Li, Bao Fei; Singh, Parampreet; Weigl, Stefan (Physical Review D, 2022)
For classical gravitational systems the lapse function and the shift vector are usually determined by imposing appropriate gauge-fixing conditions and then demanding their preservation with respect to the dynamics generated by a canonical Hamiltonian. Effective descriptions encoding quantum geometric effects motivated by loop quantum gravity for symmetry-reduced models are often captured by polymerization of connection (or related) variables in gauge-fixing conditions as well as constraints. Usually, one chooses the same form of polymerization in both cases. A pertinent question is if the dynamical stability of the effective gauge-fixing conditions under the effective dynamics generated by the polymerized canonical Hamiltonian is provided by the lapse function and the shift vector obtained from the polymerization of their classical counterparts. If this is the case, then we say that gauge fixing and polymerization commute. In this manuscript we investigate these issues and obtain consistency conditions for the commutativity of gauge fixing and polymerization. Our analysis shows that such a commutativity occurs in rather special situations and reveals pitfalls in making seemingly well-motivated choices which turn out to be inconsistent with the effective dynamics. We illustrate these findings via examples of symmetry-reduced models in the loop quantization of the Schwarzschild interior and Lemaître-Tolman-Bondi spacetimes and report the noncommutativity of gauge fixing and polymerization and inherent limitations of some choices made in the literature with a consistent effective dynamics.
CRIS-Team Scopus Importer:2022-04-29

Consistent gauge-fixing conditions in polymerized gravitational systems - Giesel, Kristina; Li, Bao-Fei; Singh, Parampreet; Weigl, Stefan (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2022)
For classical gravitational systems the lapse function and the shift vector are usually determined by imposing appropriate gauge-fixing conditions and then demanding their preservation with respect to the dynamics generated by a canonical Hamiltonian. Effective descriptions encoding quantum geometric effects motivated by loop quantum gravity for symmetry-reduced models are often captured by polymerization of connection (or related) variables in gauge-fixing conditions as well as constraints. Usually, one chooses the same form of polymerization in both cases. A pertinent question is if the dynamical stability of the effective gauge-fixing conditions under the effective dynamics generated by the polymerized canonical Hamiltonian is provided by the lapse function and the shift vector obtained from the polymerization of their classical counterparts. If this is the case, then we say that gauge fixing and polymerization commute. In this manuscript we investigate these issues and obtain consistency conditions for the commutativity of gauge fixing and polymerization. Our analysis shows that such a commutativity occurs in rather special situations and reveals pitfalls in making seemingly well-motivated choices which turn out to be inconsistent with the effective dynamics. We illustrate these findings via examples of symmetry-reduced models in the loop quantization of the Schwarzschild interior and Lemaître-Tolman-Bondi spacetimes and report the noncommutativity of gauge fixing and polymerization and inherent limitations of some choices made in the literature with a consistent effective dynamics.<br

Cosmic UHE neutrino signatures - Giesel, Kristina; Jureit, Jan-Hendrik; Reya, Ewald (Astroparticle Physics, 2003)
Utilizing the unique and reliable ultrasmall-x predictions of the dynamical (radiative) parton model, nominal event rates and their detailed energy dependence caused by a variety of cosmic UHE neutrino fluxes are calculated and analyzed. In addition, maximal Regge-model inspired small-x structure functions are employed for obtaining optimal rates which do not necessarily require 'new'physics interpretations. Upward mu(+) + mu(-) event rates are estimated by taking into account total and nadir-angle dependent regeneration effects due to neutral current interactions. For exploring extragalactic neutrino sources at highest energies (greater than or similar to 10(8) GeV) with modern (future) ground-level telescopes, we analyze horizontal air shower event rates and shower events caused by Earth-skimming tau-neutrinos, in particular their detailed shower- and cosmic neutrino-energy dependence. As an illustration of 'new physics' implications we estimate the relevant horizontal air shower event rates due to spin-2 Kaluza-Klein 'graviton' exchanges in neutral current neutrino-quark and neutrino-gluon interactions at low TeV-scales. (C) 2003 Elsevier B.V. All rights reserved.

Cosmological perturbation theory with Gaussian dust reference fields - Giesel, Kristina; Herold, Laura (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2019)

Dirac-Observablen in der Kosmolgie - Zöbelein, Carolin; Giesel, Kristina (2013)

Dynamically implementing the μ-bar-scheme in cosmological and spherically symmetric models in an extended phase space model - Giesel, Kristina; Liu, Hongguang (Universe, 2023)
We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given μ¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ¯¯-scheme can be implemented dynamically. These models are constructed in the context of the relational formalism by using a canonical transformation on the extended phase space, which provides a Kuchař decomposition of the extended phase space. The resulting model can be understood as a gauge-unfixed model of a given μ¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ¯¯-scheme. We use this formalism to investigate the restrictions to the allowed μ¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ¯¯-scheme from this perspective and discuss the differences in the cosmological and spherically symmetric case. This method can be useful, for example, to obtain a μ¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ¯¯-scheme in a top-down derivation from full LQG to symmetry-reduced effective models, where, for some models, only the μ0" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ0-scheme has been obtained thus far.<br

Dynamical Properties of the Mukhanov-Sasaki Hamiltonian - Kobler, Michael; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2018)
The inflationary epoch at the beginning of the universe is commonly described within the frame- work of (linear) cosmological perturbation theory. The corresponding equation of motion for the gauge-invariant perturbations is the Mukhanov-Sasaki equation, which resembles a time-dependent harmonic oscillator. At first we will consider a mechanical analogue of the Mukhanov-Sasaki equa- tion and use the known Lewis-Riesenfeld invariant and the extended phase space formalism in- troduced in previous works in order to analyse the system. These techniques allow to construct an extended canonical transformation that maps an explicitly time-dependent Hamiltonian into a time-independent one. The generators of this symplectic map can in turn be canonically quan- tised on the original part of the phase space, which is the constraint hypersurface of the extended theory, connecting to recent publications. Our further analysis leads us to a closed form of the time-evolution operator for the single-mode Mukhanov-Sasaki Hamiltonian, that is to the associ- ated Dyson series. We will analyse the characteristic properties of this time-evolution operator and discuss whether it can be extended to the full Fock space. Finally we give an outlook towards possible applications of these techniques to inflationary quantum cosmology.

Dynamical properties of the Mukhanov-Sasaki hamiltonian in the context of adiabatic vacua and the Lewis-Riesenfeld invariant - Fahn, Max Joseph; Giesel, Kristina; Kobler, Michael (Universe, 2019)
We use the method of the Lewis-Riesenfeld invariant to analyze the dynamical properties of the Mukhanov-Sasaki Hamiltonian and, following this approach, investigate whether we can obtain possible candidates for initial states in the context of inflation considering a quasi-de Sitter spacetime. Our main interest lies in the question of to which extent these already well-established methods at the classical and quantum level for finitely many degrees of freedom can be generalized to field theory. As our results show, a straightforward generalization does in general not lead to a unitary operator on Fock space that implements the corresponding time-dependent canonical transformation associated with the Lewis-Riesenfeld invariant. The action of this operator can be rewritten as a time-dependent Bogoliubov transformation, where we also compare our results to already existing ones in the literature. We show that its generalization to Fock space has to be chosen appropriately in order to not violate the Shale-Stinespring condition. Furthermore, our analysis relates the Ermakov differential equation that plays the role of an auxiliary equation, whose solution is necessary to construct the Lewis-Riesenfeld invariant, as well as the corresponding time-dependent canonical transformation, to the defining differential equation for adiabatic vacua. Therefore, a given solution of the Ermakov equation directly yields a full solution of the differential equation for adiabatic vacua involving no truncation at some adiabatic order. As a consequence, we can interpret our result obtained here as a kind of non-squeezed Bunch-Davies mode, where the term non-squeezed refers to a possible residual squeezing that can be involved in the unitary operator for certain choices of the Bogoliubov map.
CRIS-Team Scopus Importer:2019-08-16
Keywords: Adiabatic vacua; Bogoliubov transformation; Cosmological perturbation theory; Lewis-Riesenfeld invariant; Quantum cosmology

Dynamics of Dirac observables in canonical cosmological perturbation theory - Giesel, Kristina; Singh, Parampreet; Winnekens, David (Classical and Quantum Gravity, 2019)

Effect of loop quantization prescriptions on the physics of non-singular gravitational collapse - Giesel, Kristina; Li, Bao-Fei; Singh, Parampreet (The Sixteenth Marcel Grossmann Meeting, pp. 4267-4271 (2023), 2023)
We review recent developments in the physical implications of two loop quantization strategies for the interior of a homogeneous dust cloud. The first is the loop quantization with holonomies and the triads while the second is with holonomies and the gauge covariant fluxes. Although both of the quantization schemes resolve the classical central singularity regardless of the initial conditions, they also lead to a distinct phenomenology. For the first loop quantization, we find that when the dust mass is larger than a threshold value, both black hole and white hole would form and their evolution is symmetric with respect to the bounce point, leading to black hole-white hole twins. In contrast, in the second quantization, the evolution of the outermost dust shell is asymmetric with respect to the bounce point, and as a result the black hole-white hole twins can never form. Even in the situation when both black hole and white hole can form, the mass of the latter is only 2/π of the mass of the former.<br

Expectation Values of Holonomy-Operators in Cosmological Coherent States for Loop Quantum Gravity - Zwicknagel, Ernst-Albrecht; Giesel, Kristina; Liegener, Klaus (2018)

From classical to quantum gravity: Introduction to loop quantum gravity - Giesel, Kristina; Sahlmann, Hanno (Proceedings of Science, 2011)
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization of vacuum general relativity in loop quantum gravity.
CRIS-Team Scopus Importer:2022-05-09

From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity - Giesel, Kristina; Sahlmann, Hanno (PoS - Proceedings of Science, 2011)
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization of vacuum general relativity in loop quantum gravity.

Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase-space - A review and applications. - Giesel, Kristina; Herzog, Adrian (International Journal of Modern Physics D, 2018)
The theory of cosmological perturbations is a well elaborated field. To deal with the diffeomorphism invariance of general relativity one generally introduces combinations of the metric and matter perturbations which are gauge invariant up to the considered order in the perturbations. For linear cosmological perturbations one works with the so-called Bardeen potentials widely used in this context. However, there exists no common procedure to construct gauge invariant quantities also for higher order perturbations. Usually, one has to find new gauge invariant quantities independently for each order in perturbation theory. With the relational formalism introduced by Rovelli and further developed by Dittrich and Thiemann, it is in principle possible to calculate manifestly gauge invariant quantities, that is quantities that are gauge invariant up to arbitrary order once one has chosen a set of so-called reference fields, often also called clock fields. This article contains a review of the relational formalism and its application to canonical general relativity following the work of Garcia, Pons, Sundermeyer and Salisbury. As the starting point for our application of this formalism to cosmological perturbation theory, we also review the Hamiltonian formulation of the linearized theory for perturbations around FLRW spacetimes. The main aim of our work will be to identify clock fields in the context of the relational formalism that can be used to reconstruct quantities like the Bardeen potential as well as the Mukhanov-Sasaki variable. This requires a careful analysis of the canonical formulation in the extended ADM-phase space where lapse and shift are treated as dynamical variables. The actual construction of such observables and further investigations thereof will be carried out in our companion paper.<br
Keywords: Canonical cosmological perturbation theory; relational framework; gauge invariance; general relativity; Dirac observables.

Gauge invariant variables for cosmological perturbation theory using geometrical clocks - Giesel, Kristina; Herzog, Adrian; Singh, Parampreet (Classical and Quantum Gravity, 2018)
Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism. We show that various gauge invariant variables obtained in the conventional analysis of cosmological perturbation theory correspond to Dirac observables tied to a specific choice of geometrical clocks. As examples, we show that the Bardeen potentials and the Mukhanov-Sasaki variable emerge naturally in our analysis as observables when gauge fixing conditions are determined via clocks in the Hamiltonian framework. Similarly other gauge invariant variables for various gauges can be systematically obtained. We demonstrate this by analyzing five common gauge choices: longitudinal, spatially flat, uniform field, synchronous and comoving gauge. For all these, we apply the observable map in the context of the relational formalism and obtain the corresponding Dirac observables associated with these choices of clocks. At the linear order, our analysis generalizes the existing results in canonical cosmological perturbation theory twofold. On the one hand we can include also gauges that can only be analyzed in the context of the extended ADM-phase space and furthermore, we obtain a set of natural gauge invariant variables, namely the Dirac observables, for each considered choice of gauge conditions. Our analysis provides insights on which clocks should be used to extract the relevant natural physical observables both at the classical and quantum level. We also discuss how to generalize our analysis in a straightforward way to higher orders in the perturbation theory to understand gauge conditions and the construction of gauge invariant quantities beyond linear order.<br
Keywords: general relativity; cosmological perturbation theory; Dirac observables

Generalized analysis of a dust collapse in effective loop quantum gravity: Fate of shocks and covariance - Giesel, Kristina; Liu, Hongguang; Singh, Parampreet; Weigl, Stefan (Physical Review D, 2024)
Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such phenomenological studies have provided useful insights, questions remain on whether such models exhibit some of the desired properties such as consistent LTB conditions, covariance, and compatibility with the improved dynamics of loop quantum cosmology in the cosmological and LTB sector. We provide a systematic procedure to construct effective spherically symmetric models encoding LQG modifications as a 1+1 field theory models encoding these properties following the analysis in our companion paper [K. Giesel et al., Embedding generalized LTB models in polymerized spherically symmetric spacetimes, Phys. Rev. D 110, 104017 (2024)PRVDAQ2470-001010.1103/PhysRevD.110.104017]. As concrete examples of our generalized strategy, we obtain and compare with different phenomenological models, which have been investigated recently and demonstrate resolution of singularity by quantum geometry effects via a bounce. These include models with areal gauge fixing, a polymerized vacuum solution, polymerized junction conditions, and an Oppenheimer-Snyder dust collapse model. An important insight from our approach is that the dynamical equations care about the det(e) part rather than the square root of the determinant of the spatial metric. As a result, shock solutions that have been argued to exist in some models are found to be absent even if one considers coordinate transformations.
CRIS-Team Scopus Importer:2025-02-04

Geometrical Clocks in Cosmological Perturbation Theory - Herzog, Adrian; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2017)

Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter - Giesel, Kristina; Schuller, Frederic; Witte, Christof; Wolfarth, Matthias (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2012)
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations which are predictive, interpretable, and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry: the latter must be hyperbolic, time-orientable, and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics-for the general tensorial spacetime geometries satisfying the above minimum requirements-is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus, the search for modified gravitational dynamics is reduced to a clear mathematical task.

gravitationally induced decoherence on quantum vector fields - Kemper, Roman; Giesel, Kristina; Fahn, Max Joseph (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2023)
In this thesis we consider the coupling of Maxwell theory to linearised gravity and derive a master equation which suggests gravitationally induced decoherence on vector fields. The model is based on the linear Hamiltonian formulation of general relativity with the use of Ashtekar variables. The matter is coupled to linearised gravity, consistently using the framework of post-Minkowski formalism. In order to formulate the model at the gauge invariant level, the relational formalism is used. Therefore, we will consistently connect linearised gravity to the constrained system of Maxwell’s theory by constructing suitable geometrical and electromagnetic reference fields. This will be used to construct Dirac observables for the coupled system. Then we will use a reduced phase space quantisation on the Fock space. To construct a TCL master equation we apply the projecting operator technique with the time-convolutionless approach to the model, using a Gibbs state as the initial state for linearised gravity. All assumptions and approximations in the intermediate steps will be carefully analysed. In addition, the final TCL master equation is formulated in terms of thermal Wightmann functions and is not automatically of the Lindblad type, which is often the starting point for phenomenological models, and in contrast to the existing literature. For the derived master equation, we will also discuss why the Markov approximation is not easily applicable. Furthermore, we will motivate that the formalism used in this thesis to couple a constrained system to linearised gravity could be generalised to all Yang-Mills theories.<br
Keywords: Open quantum systems; quantum gravity; relational formalism

Gravity quantized: Loop quantum gravity with a scalar field - Giesel, Kristina; Domagala, Marcin; Kaminski, Wojciech; Lewandowski, Jerzy (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2010)
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consists of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level.

Implications from Different Regularisations for the Canonically Quantised k=1 FLRW Spacetime - Weigl, Stefan; Giesel, Kristina; Liegener, Klaus (2018)
In this work we present the regularisation of the Hamiltonian constraints in the context of the canonical description of general relativity (GR). We will start with the Hamiltonian formulation of GR and then introduce the Ashtekar-Barbero variables. After investigating the gauge trans- formations generated by the Hamiltonian constraints we present the holonomy-flux algebra where we also regularise the constraints. We will give a full derivation of the FLRW metric and then conclusively perform a regularisation for k=1 on spherical graphs.

Introduction to Dirac observables - Giesel, Kristina (International Journal of Modern Physics A, 2008)
We give a brief introduction to Dirac observables and review the general construction of such Dirac observables for constrained systems in the framework of the Relational Formalism introduced by Rovelli(1) and further mathematically developed by Dittrich.(2) Finally we birefly discuss appropriate clocks for General Relativity and the evolution of observables generated by a so called physical Hamiltonian.

Lie-Punktsymmetrien erhaltende Quantisierung in der Loop-Quantenkosmologie - Giesel, Kristina; Herzog, Adrian (2014)

Loop Quantum Gravity. The first 30 years. - Giesel, Kristina; Laddha, Alok; Varadarajan, Madhavan; Bianchi, Eugenio; Oriti, Daniele; Dittrich, Biancha; Agullo, Ivan; Singh, Parampreet; Fernando, Barbero; Perez, Alejandro; Barrau, Aurilien; Grain, Julien (World Scientific, 2017)
This volume presents a snapshot of the state-of-the-art in loop quantum gravity from the perspective of younger leading researchers. It takes the reader from the basics to recent advances, thereby bridging an important gap. The aim is two-fold — to provide a contemporary introduction to the entire field for students and post-docs, and to present an overview of the current status for more senior researchers. The contributions include the latest developments that are not discussed in existing books, particularly recent advances in quantum dynamics both in the Hamiltonian and sum over histories approaches; and applications to cosmology of the early universe and to the quantum aspects of black holes.

LTB spacetimes in terms of Dirac observables - Giesel, Kristina; Tambornino, Johannes; Thiemann, Thomas (Classical and Quantum Gravity, 2010)
The construction of Dirac observables, that is, gauge-invariant objects, in general relativity is technically more complicated than in other gauge theories such as the standard model due to its more complicated gauge group which is closely related to the group of spacetime diffeomorphisms. However, the explicit and usually cumbersome expression of Dirac observables in terms of gauge noninvariant quantities is irrelevant if their Poisson algebra is sufficiently simple. Precisely that can be achieved by employing the relational formalism and a specific type of matter proposed originally by Brown and Kuchar, namely pressureless dust fields. Moreover one is able to derive a compact expression for a physical Hamiltonian that drives their physical time evolution. The resulting gauge-invariant Hamiltonian system is obtained by Higgs-ing the dust scalar fields and has an infinite number of conserved charges which force the Goldstone bosons to decouple from the evolution. In previous publications we have shown that explicitly for cosmological perturbations. In this paper we analyse the spherically symmetric sector of the theory and it turns out that the solutions are in one-to-one correspondence with the class of Lemaitre-Tolman-Bondi metrics. Therefore, the theory is capable of properly describing the whole class of gravitational experiments that rely on the assumption of spherical symmetry.

Manifestly Gauge Invariant Cosmological Perturbation Theory - Zilker, Thomas; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2013)

Manifestly gauge-invariant general relativistic perturbation theory: I. Foundations - Giesel, Kristina; Hofmann, Stefan; Thiemann, Thomas; Winkler, Oliver (Classical and Quantum Gravity, 2010)
Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e. g. by cosmic microwave anisotropy probes. A key issue in that theory is to extract the gauge-invariant degrees of freedom which allow unambiguous comparison between theory and experiment. When one goes beyond first (linear) order, the task of writing the Einstein equations expanded to nth order in terms of quantities that are gauge-invariant up to terms of higher orders becomes highly non-trivial and cumbersome. This fact has prevented progress for instance on the issue of the stability of linear perturbation theory and is a subject of current debate in the literature. In this series of papers we circumvent these difficulties by passing to a manifestly gauge-invariant framework. In other words, we only perturb gauge-invariant, i.e. measurable quantities, rather than gauge variant ones. Thus, gauge invariance is preserved non-perturbatively while we construct the perturbation theory for the equations of motion for the gauge-invariant observables to all orders. In this first paper we develop the general framework which is based on a seminal paper due to Brown and Kuchar as well as the relational formalism due to Rovelli. In the second, companion, paper we apply our general theory to FRW cosmologies and derive the deviations from the standard treatment in linear order. As it turns out, these deviations are negligible in the late universe, thus our theory is in agreement with the standard treatment. However, the real strength of our formalism is that it admits a straightforward and unambiguous, gauge-invariant generalization to higher orders. This will also allow us to settle the stability issue in a future publication.

Manifestly gauge-invariant general relativistic perturbation theory: II. FRW background and first order - Giesel, Kristina; Hofmann, Stefan; Thiemann, Thomas; Winkler, Oliver (Classical and Quantum Gravity, 2010)
In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically coupled observer. the evolution of those observables is governed by a physical Hamiltonian and we derived the corresponding equations of motion. Linear perturbation theory of those equations of motion around a general exact solution in terms of manifestly gauge-invariant perturbations was then developed. In this paper we specialize our previous results to an FRW background which is also a solution of our modified equations of motion. We then compare the resulting equations with those derived in standard cosmological perturbation theory (SCPT). We exhibit the precise relation between our manifestly gauge-invariant perturbations and the linearly gauge-invariant variables in SCPT. We find that our equations of motion can be cast into SCPT form plus corrections. These corrections are the trace that the dust leaves on the system in terms of a conserved energy-momentum current density. In turns out that these corrections decay; in fact, in the late universe they are negligible whatever the value of the conserved current. We conclude that the addition of dust which serves as a test observer medium, while implying modifications of Einstein's equations without dust, leads to acceptable agreement with known results, while having the advantage that one now talks about manifestly gauge-invariant, that is measurable, quantities, which can be used even in perturbation theory at higher orders.

Manifestly gauge invariant perturbations of scalar-tensor theories of gravity - Han, Yu; Giesel, Kristina; Ma, Yongge (Classical and Quantum Gravity, 2015)
The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge invariant formalism is used to compute the evolution equations of linear perturbations around a general relativistic spacetime background in the Jordan frame. These equations are then specialized to the case of a flat FRW cosmological background. Furthermore, the equivalence between the Jordan frame and the Einstein frame of STT in the manifestly gauge invariant Hamiltonian formalism is analyzed, and it is shown that also in this framework they can be related by a conformal transformation. Finally, the obtained evolution equations for the linear perturbations in our formalism are compared with those in the standard cosmological perturbation theory. It turns out that the perturbation equations in the two different formalisms coincide with each other in a suitable limit.
Keywords: scalar-tensor theories of gravity; cosmological perturbation theory; manifestly gauge invariant perturbations

Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields - Giesel, Kristina; Herold, Laura; Li, Bao-Fei; Singh, Parampreet (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2020)
The aim of this article is to understand the role of dust reference fields, often also called clocks, on cosmological perturbations around a classical spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. We derive the Mukhanov-Sasaki equation for the Brown-Kuchař and Gaussian dust models, which both consider four dust fields as reference fields. The reduced phase space of Dirac observables, that is the gauge-invariant part of the theory, is constructed by means of an observable map applied to all elementary phase space variables of the coupled system, consisting of gravity, a massive scalar field and the dust degrees of freedom and automatically yields the set of independent physical variables. The evolution of these observables is governed by a so called physical Hamiltonian which can be derived once the set of reference fields are chosen and differs for each model. First, the reduced phase space for full general relativity as well as the corresponding equations of motion are derived for full general relativity. Then from this, the gauge-invariant versions of the equations of motion for the background are derived which contain a fingerprint of the dust reference fields. Afterwards we study linear cosmological perturbations around a FLRW metric using the scalar-vector-tensor decomposition and derive the equation of motion for the Mukhanov-Sasaki variable in this formalism for a chosen set of variables on the reduced phase space and expressed in terms of Dirac observables. The Mukhanov-Sasaki equation involves additional contributions that can be understood as back reactions from the dust reference fields. These additional dust contributions to the Mukhanov-Sasaki equation were absent if the dust energy and momentum density as well as their perturbations are vanishing. The nature of the correction terms suggests that Brown-Kuchař and Gaussian dust reference fields contribute differently. We numerically study the behavior of the dust contributions to the Mukhanov-Sasaki equation during inflation.<br
Keywords: Cosmological perturbation theory; Relational Formalism; Dirac Observables

Nonsingular quantum gravitational dynamics of an Lemaître-Tolman-Bondi dust shell model: The role of quantization prescriptions - Giesel, Kristina; Li, Bao-Fei; Singh, Parampreet (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2021)
We study some consequences of the loop quantization of the outermost dust shell in the Lemaître-Tolman-Bondi spacetime with a homogeneous dust density using different quantization strategies motivated by loop quantum gravity. Prior work has dealt with loop quantizing this model by employing holonomies and the triads, following the procedure in standard loop quantum cosmology. In this work we compare this quantization with the one in which holonomies and gauge-covariant fluxes are used. While both of the quantization schemes resolve the central singularity, they lead to different mass gaps at which a trapped surface forms. This trapped surface which is matched to an exterior generalized Vaidya spacetime disappears when the density of the dust cloud is in the Planck regime. We find that the quantization based on holonomies and gauge-covariant fluxes generically results in an asymmetric evolution of the dust shell in which the Vaidya mass associated with the white hole as seen by an external observer is 2/π of the one for the black hole. This effective difference in masses results from difference in the classical limits in pre- and postbounce regimes in the two quantizations. This distinctive feature rules out formation of any black-hole-white-hole twins in presence of gauge-covariant flux modifications, which is in contrast to the quantization using holonomies and triads where the gravitational collapse always leads to black hole–white hole twins. Another striking difference lies in the fact that for the quantization based on holonomies and gauge-covariant fluxes there can be situations in which during a nonsingular collapse only a black hole forms without a white hole.<br

Quantum geometry - Giesel, Kristina (Loop Quantum Gravity - The First 30 Years, 2017)
CRIS-Team Scopus Importer:2022-05-09

Quantum gravity, hydrodynamics and emergent cosmology: a collection of perspectives - Ben Achour, Jibril; Benedetti, Dario; Bojowald, Martin; Brandenberger, Robert; Butera, Salvatore; Ferrero, Renata; Giacomini, Flaminia; Giesel, Kristina; Goeller, Christophe; Haas, Tobias; A. Höhn, Philipp; Kirklin, Joshua; et al. (General Relativity and Gravitation, 2025)
This collection of perspective pieces captures recent advancements and reflections from a dynamic research community dedicated to bridging quantum gravity, hydrodynamics, and emergent cosmology. It explores four key research areas: (a) the interplay between hydrodynamics and cosmology, including analog gravity systems; (b) phase transitions, continuum limits and emergent geometry in quantum gravity; (c) relational perspectives in gravity and quantum gravity; and (d) the emergence of cosmological models rooted in quantum gravity frameworks. Each contribution presents the distinct perspectives of its respective authors. Additionally, the introduction by the editors proposes an integrative view, suggesting how these thematic units could serve as foundational pillars for a novel theoretical cosmology framework termed “hydrodynamics on superspace”.
CRIS-Team Scopus Importer:2025-01-31

Quantum gravity phenomenology at the dawn of the multi-messenger era—A review - Addazi, A.; Alvarez-Muniz, J.; Alves Batista, R.; Amelino-Camelia, G.; Antonelli, V.; Arzano, M.; Asorey, M.; Atteia, J. L.; Bahamonde, S.; Bajardi, F.; Ballesteros, A.; Baret, B.; et al. (Progress in Particle and Nuclear Physics, 2022)
The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review, prepared within the COST Action CA18108 “Quantum gravity phenomenology in the multi-messenger approach”, is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.
CRIS-Team Scopus Importer:2022-04-01
Keywords: Cosmic neutrinos; Gamma-ray astronomy; Gravitational waves; Lorentz invariance violation and deformation; Ultra-high-energy cosmic rays

Quantum Mechanics in the Polymer Particle Representation - Reichert, Thorsten; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2013)

Reduced loop quantization with four Klein-Gordon scalar fields as reference matter - Giesel, Kristina; Vetter, Almut (Classical and Quantum Gravity, 2019)
We perform a reduced phase space quantization of gravity using four Klein-Gordon scalar fields as reference matter as an alternative to the Brown-Kuchar dust model in Giesel and Thiemann (2010 Class. Quantum Grav. 27 175009), where dust scalar fields are used. We compare our results to an earlier model by Domagala et al (2010 Phys. Rev. D 82 104038) where only one Klein-Gordon scalar field is considered as reference matter for the Hamiltonian constraint but the spatial diffeomorphism constraints are quantized using Dirac quantization. As a result we find that the choice of four conventional Klein-Gordon scalar fields as reference matter leads to a reduced dynamical model that cannot be quantized using loop quantum gravity techniques. However, we further discuss a slight generalization of the action for the four Klein-Gordon scalar fields and show that this leads to a model which can be quantized in the framework of loop quantum gravity. By comparison of the physical Hamiltonian operators obtained from the model by Domagala et al (2010 Phys. Rev. D 82 104038) and the one introduced in this work we are able to make a first step towards comparing Dirac and reduced phase space quantization in the context of the spatial diffeomorphism constraints.
CRIS-Team Scopus Importer:2019-08-02
Keywords: Dirac observables; loop quantum gravity; reduced phase space quantization

Regular black holes and their relationship to polymerized models and mimetic gravity - Giesel, Kristina; Liu, Hongguang; Singh, Parampreet; Weigl, Stefan (Physical Review D, 2025)
We present further applications of the formalism introduced by K. H. Akinori Tanaka and Akio Tomiya in [Deep Learning and Phyiscs (Springer, Switzerland, 2021)], which allows the embedding of a broad class of generalized Lemaître-Tolmann-Bondi (LTB) models into effective spherically symmetric spacetimes. We focus on regular black hole models, where a broad class of models can be considered, including for example loop quantum gravity (LQG)-inspired models as well as models with a regular center, e.g., of Bardeen and Hayward. For a certain class of regular black hole models, we can formulate a Birkhoff-like theorem in LTB coordinates. We further show that, depending on the properties of the polymerization functions characterizing such regular black hole models in this formalism, the uniqueness of the effective spherically symmetric vacuum solutions might not be given in general in Schwarzschild-like coordinates. Furthermore, we introduce a reconstruction algorithm that allows for a subclass of these models to construct from a given metric in Schwarzschild-like coordinates the corresponding effective spherically symmetric model, its dynamics as a 1+1-dimensional field theory, as well as a corresponding covariant Lagrangian of extended mimetic gravity in four dimensions. Such a reconstruction allows us to obtain Lagrangians of extended mimetic gravity models for black holes with a regular center, e.g., the Bardeen and Hayward metric, as well as for effective LQG inspired models. Moreover, the reconstruction enables us to extend regular black hole models to general inhomogeneous dust collapse models. For the latter, within this formalism, we can investigate and explore various physical properties of the models such as the existence of weak shell-crossing singularities from a novel perspective.
CRIS-Team Scopus Importer:2025-04-04

Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory - Giesel, Kristina; Li, Bao-Fei; Singh, Parampreet (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2021)
Models with dust reference fields in relational formalism have proved useful in understanding the construction of gauge invariant perturbation theory to arbitrary orders in the canonical framework. These reference fields modify the dynamical equations for perturbation equations. However, important questions remain open on the relation with conventional perturbation theories of inflaton coupled to gravity and of multifluid systems, and on understanding modifications in terms of physical degrees of freedom. These gaps are filled in this manuscript for Brown-Kuchař and Gaussian dust models, both of which involve three scalar physical degrees of freedom. We establish a relationship of these models with conventional inflationary and multifluid systems of inflation and ordinary dust by introducing a set of gauge invariant variables on the reduced phase space of the dust reference models. We find the modifications due to dust clocks to the Bardeen equation in the longitudinal gauge and the Mukhanov-Sasaki equation in the spatially flat gauge, in terms of physical degrees of freedom. This results in a closed system of equations for all the degrees of freedom needed to explore the evolution of the scalar perturbations. Our analysis shows for the first time that even for two-fluid systems, there is a natural choice of the set of gauge invariant variables for each chosen gauge which not only offers a direct physical interpretation but also results in simplifications to the dynamical equations.<br
Keywords: Cosmology; Cosmological Perturbation Theory

Revisiting a 4-Scalar Fields Reference Model in the Context of a Loop Quantization - Weigl, Stefan; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2021)

Scalar material reference systems and loop quantum gravity - Giesel, Kristina; Thiemann, Thomas (Classical and Quantum Gravity, 2015)
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasized frequently. This idea has been picked up more recently in loop quantum gravity with the aim to perform a reduced phase space quantization of the theory, thus possibly avoiding problems with the (Dirac) operator constraint quantization method for a constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrize the space of theories considered so far. We then describe the quantum theory of a model that, to the best of our knowledge, has only been considered classically so far. This model could arguably be called the optimal one in this class of models considered as it displays the simplest possible true Hamiltonian, while at the same time reducing all constraints of general relativity.
Keywords: scalar material reference systems; loop quantum gravity; Dirac observables

Semiclassical Perturbation Theory within Loop Quantum Gravity - Winnekens, David; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2014)

Spherical symmetric gravitational collapse of a dust cloud: Polymerized dynamics in reduced phase space - Giesel, Kristina; Han, Muxin; Li, Bao Fei; Liu, Hongguang; Singh, Parampreet (Physical Review D, 2023)
Based on the effective dynamics in the μ¯ scheme of the spherical symmetry reduced model in the reduced phase space formulation of loop quantum gravity (LQG), we investigate the gravitational collapse of a homogeneous dust cloud, with Gaussian dust serving as both the reference field and the source of the gravitational collapse. The effective dynamics from the considered model for a homogeneous dust cloud reduces precisely to the effective dynamics of loop quantum cosmology (LQC) with extrinsic curvature based K-quantization, indicating that the LQC effective dynamics lives as a subsector of the model presented here. In both the marginally bound and the bound cases of the collapse in effective dynamics, the singularity is resolved and replaced by a bounce. Though quantum geometric modification from spatial curvature is not directly included in the K-quantization it does affect the qualitative dynamics of the collapsing dust cloud in the sense that on the one hand for the marginally bound case, the dust cloud bounces once at fixed maximum energy density and on the other hand for the bound case, the dust cloud undergoes infinite cycles of contraction and expansion at energy densities dependent on the dust mass. Finally, the mass threshold for the formation of a trapped surface in each case is found and the matching conditions between the interior collapsing spacetime and an effective exterior static solution are discussed.
Created from Fastlane, Scopus look-up

The Lewis-Riesenfeld Invariant in the context of a Loop Quantum Cosmology quantisation - Matas, Bystrik; Giesel, Kristina; Kobler, Michael (2018)

The Physical Hamiltonian of the Gowdy Model in Algebraic Quantum Gravity - Böhm, Benedikt; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2015)

The Schrödinger Equation of the Gowdy Model in Reduced Algebraic Quantum Gravity - Leitherer, Andreas; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2017)

The Spin-Boson Model with a time-dependent Oscillator Environment - Banarescu, Marvin; Kobler, Michael; Giesel, Kristina (2021)

Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential. - Giesel, Kristina; Li, Bao-Fei; Singh, Parampreet (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2020)
We explore a reduced phase space quantization of loop quantum cosmology (LQC) for a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe filled with reference fields and an inflaton field in a Starobinsky inflationary potential. We consider three separate cases in which the reference fields are taken to be the Gaussian dust, the Brown-Kuchař dust, and massless Klein-Gordon scalar reference fields respectively. This is a “two-fluid” model in which reference fields act as global clocks providing a physical time in an inflationary spacetime, and allow bypassing various technical hurdles in conventional quantum cosmological models. The reduced phase space is obtained in terms of the Dirac observables of the gravitational as well as the inflaton degrees of freedom. The physical Hamiltonians of the two dust models take the same form but turn out to be quite different from that of the Klein-Gordon reference field which reflects an aspect of the multiple choice problem of time. Loop quantization is implemented using the so-called ¯μ scheme and the Schrödinger equations involving the physical Hamiltonian operators generating the evolution in the physical time in the dust and massless Klein-Gordon models are obtained. These turn out to be quantum difference equations with the same nonsingular structure as for other models in LQC. We study some phenomenological implications of the quantization using the effective dynamics resulting from the reduced phase space quantization including the resolution of the big bang singularity via a quantum bounce, and effects of the different reference fields on e-foldings in both the preinflationary and the slow-roll inflationary phases. We find that different clocks, even when starting with a small but same energy density, can leave tiny but different imprints on the inflationary dynamics. In addition, for Brown-Kuchař dust, the choice of a negative energy density can result in a cyclic evolution before the onset of inflation constraining certain values for ideal clocks.<br

Understanding gravitationally induced decoherence parameters in neutrino oscillations using a microscopic quantum mechanical model - Domi, Alba; Eberl, Thomas; Fahn, Max Joseph; Giesel, Kristina; Hennig, Lukas; Katz, Uli; Kemper, Roman; Kobler, Michael (Journal of Cosmology and Astroparticle Physics, 2024)
In this work, a microscopic quantum mechanical model for gravitationally induced decoherence introduced by Blencowe and Xu is investigated in the context of neutrino oscillations. The focus is on the comparison with existing phenomenological models and the physical interpretation of the decoherence parameters in such models. The results show that for neutrino oscillations in vacuum gravitationally induced decoherence can be matched with phenomenological models with decoherence parameters of the form Γij ∼ Δ m 4ij E -2. When matter effects are included, the decoherence parameters exhibit a dependence on the varying matter density across the Earth layers. This behavior can be explained by the nature of the coupling between neutrinos and the gravitational wave environment, as suggested by linearised gravity. On a theoretical level, these different models can be characterised by a different choice of Lindblad operators, with the model with decoherence parameters that do not include matter effects being less suitable from the point of view of linearised gravity. Consequently, in the case of neutrino oscillations in matter, the microscopic model does not agree with many existing phenomenological models that assume constant decoherence parameters in matter. Nonetheless, we identify the KamLAND experimental setup as particularly well-suited to establish the first experimental constraints on the model parameters, namely the neutrino coupling to the gravitational wave environment and its temperature, based on a prior analysis using the phenomenological model.
CRIS-Team Scopus Importer:2024-11-22
Keywords: gravity; neutrino experiments; neutrino theory; solar and atmospheric neutrinos