Extensions of the Duflo map and Chern-Simons expectation values - Sahlmann, Hanno; Zilker, Thomas (Journal of Geometry and Physics, 2017)
The Duflo map is a valuable tool for operator ordering in contexts in which Kirillov-Kostant brackets and their quantizations play a role. A priori, the Duflo map is only defined on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. Here we discuss extensions to the whole symmetric algebra, as well as their application to the calculation of Chern-Simons theory expectation values.

Geometry and entanglement entropy of surfaces in loop quantum gravity - Sahlmann, Hanno; Grüber, David; Zilker, Thomas (Physical Review D, 2018)

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

Quantum Simplicity Constraints and Area Spectrum - Zilker, Thomas; Thiemann, Thomas (2010)

Quantum surface holonomies for loop quantum gravity and their application to black hole horizons - Sahlmann, Hanno; Zilker, Thomas (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2020)
In this work we define a new type of flux operators on the Hilbert space of loop quantum gravity. We use them to solve an equation of the form F(A) = c Sigma in loop quantum gravity. This equation, which relates the curvature of a connection A with its canonical conjugate Sigma = *E, plays an important role for spherically symmetric isolated horizons, and, more generally, for maximally symmetric geometries and for the Kodama state. If the equation holds, the new flux operators can be interpreted as a quantization of surface holonomies from higher gauge theory. Also, they represent a kind of quantum deformation of SU(2). We investigate their properties and discuss how they can be used to define states that satisfy the isolated horizon boundary condition in the quantum theory.
CRIS-Team WoS Importer:2020-07-24