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Published March 10, 2019 | Version Published + Submitted
Journal Article Open

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

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Brandeis University
  • 3. ROR icon University of Oxford

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.

Additional Information

© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 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.

Attached Files

Published - 1-s2.0-S0370269319300966-main.pdf

Submitted - 1811.03124.pdf

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Additional details

Additional titles

Alternative title
Do all identically conserved geometric tensors come from actions? A status report

Identifiers

Eprint ID
91036
Resolver ID
CaltechAUTHORS:20181119-151633175

Related works

Describes
https://arxiv.org/abs/1811.03124 (URL)

Funding

Department of Energy (DOE)
DE-SC0011632
Royal Society
SCOAP3

Dates

Created
2018-11-19
Created from EPrint's datestamp field
Updated
2021-11-16
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Walter Burke Institute for Theoretical Physics
Other Numbering System Name
CALT-TH
Other Numbering System Identifier
2018-046