Quantum geometrodynamics revived I. Classical constraint algebra

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 quant...

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Bibliographic Details
Published in:Classical and quantum gravity 2024-09, Vol.41 (18), p.185004
Main Authors: Lang, Thorsten, Schander, Susanne
Format: Article
Language:English
Subjects:
constraints
geometrodynamics
gravity
lattice
metric
quantum
quantum field theory
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Summary: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.
ISSN:0264-9381
1361-6382
DOI:10.1088/1361-6382/ad41b1