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Non-relativistic geometry and the equivalence principle

Kapustin, Anton and Touraev, Marc (2021) Non-relativistic geometry and the equivalence principle. Classical and Quantum Gravity, 38 (13). Art. No. 135003. ISSN 0264-9381. doi:10.1088/1361-6382/abfea5. https://resolver.caltech.edu/CaltechAUTHORS:20210608-073034132

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Abstract

We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a curved and time-dependent spatial metric. It is this requirement that forces the gravitational mass to be equal to the inertial mass. We identify the symmetry responsible for the equivalence principle as the remnant of time-reparameterization symmetry of the relativistic theory. We also clarify the transformation properties of the Schrödinger wave-function under arbitrary frame changes.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/1361-6382/abfea5DOIArticle
https://arxiv.org/abs/2101.04153arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2021 IOP Publishing Ltd. Received 23 January 2021; Revised 13 April 2021; Accepted 6 May 2021; Published 1 June 2021. MT is grateful to the Caltech SURF program for providing a research opportunity. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. AK was also supported by the Simons Investigator Award. Data availability statement: No new data were created or analysed in this study.
Funders:
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Subject Keywords:equivalence principle, Schrödinger equation, Ehresmann connection
Issue or Number:13
DOI:10.1088/1361-6382/abfea5
Record Number:CaltechAUTHORS:20210608-073034132
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210608-073034132
Official Citation:Anton Kapustin and Marc Touraev 2021 Class. Quantum Grav. 38 135003
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109429
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jun 2021 19:29
Last Modified:09 Jun 2021 19:29

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