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Title: Are all identically conserved geometric tensors metric variations of actions? A status report

Abstract

Noether's theorem, that local gauge variations of gauge invariant actions are identically conserved (more tautologically, that gauge variations of gauge invariants vanish) was established a century ago. Its converse, in the geometric context: are all identically conserved local symmetric tensors variations of some coordinate invariant action? remains unsolved to this day. We survey its present state and discuss some of our concrete attempts at a solution, including a significant improvement. For notational simplicity, details are primarily given in D=2, but we discuss generic D as well.

Authors:
; ORCiD logo
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); UK Royal Society
OSTI Identifier:
1547784
Alternate Identifier(s):
OSTI ID: 1596469
Grant/Contract Number:  
SC0011632; NF170385
Resource Type:
Published Article
Journal Name:
Physics Letters B
Additional Journal Information:
Journal Name: Physics Letters B Journal Volume: 790 Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Country of Publication:
Netherlands
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; General relativity; Conservation laws

Citation Formats

Deser, S., and Pang, Y. Are all identically conserved geometric tensors metric variations of actions? A status report. Netherlands: N. p., 2019. Web. doi:10.1016/j.physletb.2019.02.005.
Deser, S., & Pang, Y. Are all identically conserved geometric tensors metric variations of actions? A status report. Netherlands. doi:10.1016/j.physletb.2019.02.005.
Deser, S., and Pang, Y. Fri . "Are all identically conserved geometric tensors metric variations of actions? A status report". Netherlands. doi:10.1016/j.physletb.2019.02.005.
@article{osti_1547784,
title = {Are all identically conserved geometric tensors metric variations of actions? A status report},
author = {Deser, S. and Pang, Y.},
abstractNote = {Noether's theorem, that local gauge variations of gauge invariant actions are identically conserved (more tautologically, that gauge variations of gauge invariants vanish) was established a century ago. Its converse, in the geometric context: are all identically conserved local symmetric tensors variations of some coordinate invariant action? remains unsolved to this day. We survey its present state and discuss some of our concrete attempts at a solution, including a significant improvement. For notational simplicity, details are primarily given in D=2, but we discuss generic D as well.},
doi = {10.1016/j.physletb.2019.02.005},
journal = {Physics Letters B},
number = C,
volume = 790,
place = {Netherlands},
year = {2019},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1016/j.physletb.2019.02.005

Citation Metrics:
Cited by: 2 works
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