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Title: Noether’s 1st theorem with local symmetries
Authors: Aoki, Sinya
Author's alias: 青木, 愼也
Keywords: A02 Other topics in general physics
B00 Lattice gauge field theories
E00 Gravity in general
Issue Date: Dec-2022
Publisher: Oxford University Press (OUP)
Journal title: Progress of Theoretical and Experimental Physics
Volume: 2022
Issue: 12
Thesis number: 123A02
Abstract: Noether’s 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved currents. In this paper, we propose a general method to derive a matter-conserved current associated with a special global symmetry in the presence of local symmetries. While currents derived from local symmetries of a matter sector with a covariant background gauge field are not conserved in general, we show that the current associated with a special type of a global symmetry, called a hidden matter symmetry, is on-shell conserved. We apply this derivation to a U(1) gauge theory, general relativity and non-abelian gauge theory. In general relativity, the associated conserved charge agrees with the one recently proposed from a different point of view.
Rights: © The Author(s) 2022. Published by Oxford University Press on behalf of the Physical Society of Japan.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Funded by SCOAP3. SCOAP3 and OUP support the goals of the International Year of Basic Sciences for Sustainable Development
URI: http://hdl.handle.net/2433/285354
DOI(Published Version): 10.1093/ptep/ptac160
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