Hawking Radiation - Lang, Thorsten; et al. (2011)

Peakedness properties of SU(3) heat kernel coherent states - Lang, Thorsten; Thiemann, Thomas (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2015)

Quantum geometrodynamics revived I. Classical constraint algebra - Lang, Thorsten; Schander, Susanne (Classical and Quantum Gravity, 2024)
In this series of papers, we present a set of methods to revive quantum geometrodynamics which encountered numerous mathematical and conceptual challenges in its original form promoted by Wheeler and De Witt. In this paper, we introduce the regularization scheme on which we base the subsequent quantization and continuum limit of the theory. Specifically, we employ the set of piecewise constant fields as the phase space of classical geometrodynamics, resulting in a theory with finitely many degrees of freedom of the spatial metric field. As this representation effectively corresponds to a lattice theory, we can utilize well-known techniques to depict the constraints and their algebra on the lattice. We are able to compute the lattice corrections to the constraint algebra. This model can now be quantized using the usual methods of finite-dimensional quantum mechanics, as we demonstrate in the following paper. The application of the continuum limit is the subject of a future publication.
CRIS-Team Scopus Importer:2024-08-30
Keywords: constraints; geometrodynamics; gravity; lattice; metric; quantum; quantum field theory

Quantum geometrodynamics revived: II. Hilbert space of positive definite metrics - Lang, Thorsten; Schander, Susanne (Classical and Quantum Gravity, 2024)
This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a lattice regularization of the hypersurface deformation algebra, such that each lattice site carries a set of canonical variables given by the components of the spatial metric and the corresponding conjugate momenta. In order to quantize this theory, we describe a representation of the canonical commutation relations that enforces the positivity of the operators q ^ a b s a s b for all choices of s. Moreover, symmetry of q ^ a b and p ^ a b is ensured. This reflects the physical requirement that the spatial metric should be a positive definite, symmetric tensor. To achieve this end, we resort to the Cholesky decomposition of the spatial metric into upper triangular matrices with positive diagonal entries. Moreover, our Hilbert space also carries a representation of the vielbein fields and naturally separates the physical and gauge degrees of freedom. Finally, we introduce a generalization of the Weyl quantization for our representation. We want to emphasize that our proposed methodology is amenable to applications in other fields of physics, particularly in scenarios where the configuration space is restricted by complicated relationships among the degrees of freedom.
CRIS-Team Scopus Importer:2024-08-30
Keywords: geometrodynamics; gravity; metric; quantum