Quantum geometrodynamics revived I. Classical constraint algebra

Lang T, Schander S (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Classical and Quantum Gravity Institute of Physics: Hybrid Open Access

Book Volume: 41

Article Number: 185004

Journal Issue: 18

DOI: 10.1088/1361-6382/ad41b1

Abstract

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.

Authors with CRIS profile

Thorsten Lang Chair for Theoretical Physics III (Quantum Gravity)

Involved external institutions

Perimeter Institute for Theoretical Physics CA Canada (CA)

How to cite

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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