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

Deser, S. and Pang, Y. (2019) Are all identically conserved geometric tensors metric variations of actions? A status report. Physics Letters B, 790 . pp. 533-536. ISSN 0370-2693. doi:10.1016/j.physletb.2019.02.005.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Deser, S.0000-0001-9285-9434
Alternate Title:Do all identically conserved geometric tensors come from actions? A status report
Additional Information:© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( Funded by SCOAP3. Received 14 November 2018, Revised 16 January 2019, Accepted 6 February 2019, Available online 8 February 2019. We thank Andrew Waldron for his useful suggestions in the early stages of this endless saga. The work of S.D. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The work of Y.P. is supported by a Newton International Fellowship of the UK Royal Society.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Subject Keywords:General relativity; Conservation laws
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Record Number:CaltechAUTHORS:20181119-151633175
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Official Citation:S. Deser, Y. Pang, Are all identically conserved geometric tensors metric variations of actions? A status report, Physics Letters B, Volume 790, 2019, Pages 533-536, ISSN 0370-2693, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91036
Deposited By: Joy Painter
Deposited On:19 Nov 2018 23:35
Last Modified:16 Nov 2021 03:37

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