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@masterthesis{faucris.122308384,
author = {Thurn, Andreas and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Constraint} {Analysis} of the {D}+1 dimensional {Palatini} action},
year = {2009}
}
@phdthesis{faucris.121044704,
author = {Thurn, Andreas and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Higher} {Dimensional} and {Supersymmetric} {Extensions} of {Loop} {Quantum} {Gravity}},
year = {2013}
}
@article{faucris.110413644,
abstract = {Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one's disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauss, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045001},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {I}. {Hamiltonian} analysis},
volume = {30},
year = {2013}
}
@article{faucris.108346964,
abstract = {We quantize the new connection formulation of (D + 1)-dimensional general relativity developed in our companion papers by loop quantum gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalize to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its 'diagonal' components acting at edges of spin-network functions are easily solved, its 'off-diagonal' components acting at vertices are non-trivial and require a more elaborate treatment.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045003},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {III}. {Quantum} theory},
volume = {30},
year = {2013}
}
@article{faucris.123223364,
abstract = {We rederive the results of our companion paper, for matching space-time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the Palatini action contains second class constraints, by an appeal to the method of gauge unfixing, we map the second class system to an equivalent first class system which turns out to be identical to the first class constraint system obtained via the extension of the ADM phase space performed in our companion paper. Central to our analysis is again the appropriate treatment of the simplicity constraint. Remarkably, the simplicity constraint invariant extension of the Hamiltonian constraint, that is a necessary step in the gauge unfixing procedure, involves a correction term which is precisely the one found in the companion paper and which makes sure that the Hamiltonian constraint derived from the Palatini Lagrangian coincides with the ADM Hamiltonian constraint when Gauss and simplicity constraints are satisfied. We therefore have rederived our new connection formulation of general relativity from an independent starting point, thus confirming the consistency of this framework.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045002},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {II}. {Lagrangian} analysis},
volume = {30},
year = {2013}
}
@article{faucris.110414744,
abstract = {We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv: 1105.3703 [gr-qc]; arXiv: 1105.3704 [gr-qc]; arXiv: 1105.3705 [gr-qc]) to derive a connection formulation of Lorentzian general relativity coupled to Dirac fermions in dimensions D + 1 >= 3 with a compact gauge group. The technique that accomplishes that is similar to the one that has been introduced in 3+1 dimensions already. First one performs a canonical analysis of Lorentzian general relativity using the time gauge and then introduces an extension of the phase space analogous to the one employed in [1] to obtain a connection theory with SO(D + 1) as the internal gauge group subject to additional constraints. The success of this method rests heavily on the strong similarity of the Lorentzian and Euclidean Clifford algebras. A quantization of the Hamiltonian constraint is provided.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045004},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {IV}. {Matter} coupling},
volume = {30},
year = {2013}
}
@article{faucris.123223584,
abstract = {In this paper, we generalize the treatment of isolated horizons in loop quantum gravity, resulting in a Chern-Simons theory on the boundary in the four-dimensional case, to non-distorted isolated horizons in 2(n + 1)-dimensional spacetimes. The key idea is to generalize the four-dimensional isolated horizon boundary condition by using the Euler topological density E-(2n) of a spatial slice of the black hole horizon as a measure of distortion. The resulting symplectic structure on the horizon coincides with the one of higher-dimensional SO(2(n + 1))-Chern-Simons theory in terms of a Peldan-type hybrid connection Gamma(0) and resembles closely the usual treatment in (3 + 1) dimensions. We comment briefly on a possible quantization of the horizon theory. Here, some subtleties arise since higher-dimensional non-Abelian Chern-Simons theory has local degrees of freedom. However, when replacing the natural generalization to higher dimensions of the usual boundary condition by an equally natural stronger one, it is conceivable that the problems originating from the local degrees of freedom are avoided, thus possibly resulting in a finite entropy.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/31/5/055002},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {loop quantum gravity;higher dimensions;black holes;Chern-Simons theory},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {V}. {Isolated} horizon boundary degrees of freedom},
volume = {31},
year = {2014}
}
@article{faucris.110416284,
abstract = {In this paper, we discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional general relativity and supergravity developed in our companion papers. Since the canonical quadratic simplicity constraint operators have been shown to be anomalous in any dimension D >= 3 in Class. Quantum Grav. 30 045003, non-standard methods have to be employed to avoid inconsistencies in the quantum theory. We show that one can choose a subset of quadratic simplicity constraint operators which are non-anomalous among themselves and allow for a natural unitary map of the spin networks in the kernel of these simplicity constraint operators to the SU(2)-based Ashtekar-Lewandowski Hilbert space in D = 3. The linear constraint operators on the other hand are non-anomalous by themselves; however, their solution space is shown to differ in D = 3 from the expected Ashtekar-Lewandowski Hilbert space. We comment on possible strategies to make a connection to the quadratic theory. Also, we comment on the relation of our proposals to the existing work in the spin foam literature and how these works could be used in the canonical theory. We emphasize that many ideas developed in this paper are certainly incomplete and should be considered as suggestions for possible starting points for more satisfactory treatments in the future.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045005},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{On} the implementation of the canonical quantum simplicity constraint},
volume = {30},
year = {2013}
}
@article{faucris.123229524,
abstract = {Should nature be supersymmetric, then it will be described by Quantum Supergravity at least in some energy regimes. The currently most advanced description of Quantum Supergravity and beyond is Superstring Theory/M-Theory in 10/11 dimensions. String Theory is a top-to-bottom approach to Quantum Supergravity in that it postulates a new object, the string, from which classical Supergravity emerges as a low energy limit. On the other hand, one may try more traditional bottom-to-top routes and apply the techniques of Quantum Field Theory. Loop Quantum Gravity (LQG) is a manifestly background independent and non-perturbative approach to the quantisation of classical General Relativity, however, so far mostly without supersymmetry. The main obstacle to the extension of the techniques of LQG to the quantisation of higher dimensional Supergravity is that LQG rests on a specific connection formulation of General Relativity which exists only in D + 1 = 4 dimensions. In this Letter we introduce a new connection formulation of General Relativity which exists in all space-time dimensions. We show that all LQG techniques developed in D + 1 = 4 can be transferred to the new variables in all dimensions and describe how they can be generalised to the new types of fields that appear in Supergravity theories as compared to standard matter, specifically Rarita-Schwinger and p-form gauge fields. (C) 2012 Elsevier B.V. All rights reserved.},
author = {Bodendorfer, Norbert and Thurn, Andreas and Thiemann, Thomas},
doi = {10.1016/j.physletb.2012.04.003},
faupublication = {yes},
journal = {Physics Letters B},
keywords = {Loop quantum gravity;Supergravity;Higher dimensional gravity},
pages = {205-211},
peerreviewed = {Yes},
title = {{Towards} {Loop} {Quantum} {Supergravity} ({LQSG})},
volume = {711},
year = {2012}
}
@article{faucris.123229964,
abstract = {In our companion paper, we focused on the quantization of the Rarita-Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime dimensions. In this paper, we extend this analysis by considering the quantization of additional bosonic fields necessary to obtain a complete SUSY multiplet next to graviton and gravitino in various dimensions. As a generic example, we study concretely the quantization of the 3-index photon of minimal 11d SUGRA, but our methods easily extend to more general p-form fields. Due to the presence of a Chern-Simons term for the 3-index photon, which is due to local SUSY, the theory is self-interacting and its quantization far from straightforward. Nevertheless, we show that a reduced phase space quantization with respect to the 3-index photon Gauss constraint is possible. Specifically, the Weyl algebra of observables, which deviates from the usual CCR Weyl algebras by an interesting twist contribution proportional to the level of the Chern-Simons theory, admits a background independent state of the Narnhofer-Thirring type.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045007},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Towards} loop quantum supergravity ({LQSG}): {II}. p-form sector},
volume = {30},
year = {2013}
}
@article{faucris.123229744,
abstract = {In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is Poisson-commuting, which implies that loop quantum gravity quantization methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature supergravity theories, in particular 11D SUGRA and 4D, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in the presence of the Rarita-Schwinger field. This is non-trivial because SUSY typically requires the Rarita-Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signatures. We resolve the arising tension and provide a background-independent representation of the non-trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045006},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Towards} loop quantum supergravity ({LQSG}): {I}. {Rarita}-{Schwinger} sector},
volume = {30},
year = {2013}
}