Lang T, Schander S (2024)
Publication Type: Journal article
Publication year: 2024
Book Volume: 41
Article Number: 185004
Journal Issue: 18
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.
APA:
Lang, T., & Schander, S. (2024). Quantum geometrodynamics revived I. Classical constraint algebra. Classical and Quantum Gravity, 41(18). https://doi.org/10.1088/1361-6382/ad41b1
MLA:
Lang, Thorsten, and Susanne Schander. "Quantum geometrodynamics revived I. Classical constraint algebra." Classical and Quantum Gravity 41.18 (2024).
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