Calcinari, A. orcid.org/0000-0003-3028-0587 and Gielen, S. orcid.org/0000-0002-8653-5430 (2025) Relational dynamics and Page-Wootters formalism in group field theory. Quantum, 9. 1610. ISSN 2521-327X
Abstract
Group field theory posits that spacetime is emergent and is hence defined without any background notion of space or time; dynamical questions are formulated in relational terms, in particular using (scalar) matter degrees of freedom as time. Unlike in canonical quantisation of gravitational systems, there is no obvious notion of coordinate transformations or constraints, and established quantisation methods cannot be directly applied. As a result, different canonical formalisms for group field theory have been discussed in the literature. We address these issues using a parametrised version of group field theory, in which all (geometry and matter) degrees of freedom evolve in a fiducial parameter. There is a constraint associated to the freedom of reparametrisation and the Dirac quantisation programme can be implemented. Using the "trinity of relational dynamics", we show that the resulting "clock-neutral" theory is entirely equivalent to a deparametrised canonical group field theory, interpreted in terms of the Page-Wootters formalism. Our results not only show that the deparametrised quantisation is fully covariant and can be seen as encoding the dynamics of joint quantum matter and geometry degrees of freedom, they also appear to be the first application of the Page-Wootters formalism directly to non-perturbative quantum gravity. We show extensions to a setting in which many independent gauge symmetries are introduced, which connects to the "multi-fingered time" idea in quantum gravity and provides a somewhat novel extension of the Page-Wootters formalism.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0 - https://creativecommons.org/licenses/by/4.0/) license. Copyright remains with the original copyright holders such as the authors or their institutions. |
Keywords: | Nuclear and Plasma Physics; Particle and High Energy Physics; Mathematical Physics; Mathematical Sciences; Physical Sciences |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Feb 2025 15:01 |
Last Modified: | 14 Feb 2025 15:01 |
Status: | Published |
Publisher: | Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften |
Refereed: | Yes |
Identification Number: | 10.22331/q-2025-01-27-1610 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:223285 |