Gielen, S. orcid.org/0000-0002-8653-5430 and Wise, D.K. (2012) Spontaneously broken Lorentz symmetry for Hamiltonian gravity. Physical Review D, 85 (10). ISSN 2470-0010
Abstract
In Ashtekar’s Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields, presenting a significant obstacle to quantization, or additional (usually second class) constraints whose solution renders the resulting phase space variables harder to interpret in a spacetime picture. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation in which second class constraints never arise. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3, 1) symmetry down to a subgroup SO(3)y. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as “Cartan geometrodynamics.” We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3, 1) to SO(3) is not in conflict with Lorentz covariance.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2012 American Physical Society. This is an author-produced version of a paper subsequently published in Physical Review D. Uploaded in accordance with the publisher's self-archiving policy. |
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: | 08 Oct 2019 13:35 |
Last Modified: | 08 Oct 2019 14:31 |
Status: | Published |
Publisher: | American Physical Society (APS) |
Refereed: | Yes |
Identification Number: | 10.1103/physrevd.85.104013 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:151742 |