Gielen, S. orcid.org/0000-0002-8653-5430 (2021) Frozen formalism and canonical quantization in (group) field theory. Physical Review D, 104 (10). 106011. ISSN 2470-0010
Abstract
Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears “frozen.” Two strategies towards the quantization of such systems are the identification of a clock degree of freedom before quantization (deparametrization), and quantization on a kinematical Hilbert space which is subject to constraints (Dirac quantization). The usual canonical quantization in quantum field theory is analogous to deparametrization. Here we introduce a frozen formalism and Dirac quantization for a complex Klein–Gordon scalar field, and show that the resulting theory is equivalent to usual canonical quantization. We then apply the formalism to the group field theory formalism for quantum gravity, for which both deparametrization and a “timeless” quantization have been proposed in past work. We show how a frozen formalism for group field theory links between these two existing approaches, and illustrate in particular the construction of physical observables. We derive effective cosmological dynamics for group field theory in the new formalism and compare these to previous work. The frozen formalism could be extended to other approaches to quantum gravity that do not use a preferred time parameter.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. |
Keywords: | canonical quantization; group field theory; problem of time; Dirac quantization |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Nov 2021 16:00 |
Last Modified: | 17 Nov 2021 09:52 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevD.104.106011 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:179991 |