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

Deser, S.; Pang, Y.

doi:10.1016/j.physletb.2019.02.005

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:

Deser, S.;

Publication Date:: 2019-03-01

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); 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.

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                    Deser, S., & Pang, Y.. Are all identically conserved geometric tensors metric variations of actions? A status report.  Netherlands.  https://doi.org/10.1016/j.physletb.2019.02.005

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                    Deser, S., and Pang, Y.. Fri .  
"Are all identically conserved geometric tensors metric variations of actions? A status report".  Netherlands.  https://doi.org/10.1016/j.physletb.2019.02.005.

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@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}

}

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Works referenced in this record:

Variational principles for natural divergence-free tensors in metric field theories
journal, December 2012

Anderson, Ian M.; Pohjanpelto, Juha
Journal of Geometry and Physics, Vol. 62, Issue 12
DOI: 10.1016/j.geomphys.2012.08.003

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Bekenstein, Jacob D.; Majhi, Bibhas Ranjan
Nuclear Physics B, Vol. 892
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Minimal massive 3D gravity
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Bergshoeff, Eric; Hohm, Olaf; Merbis, Wout
Classical and Quantum Gravity, Vol. 31, Issue 14
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A Remarkable Property of the Riemann-Christoffel Tensor in Four Dimensions
journal, October 1938

Lanczos, Cornelius
The Annals of Mathematics, Vol. 39, Issue 4
DOI: 10.2307/1968467

The Einstein Tensor and Its Generalizations
journal, March 1971

Lovelock, David
Journal of Mathematical Physics, Vol. 12, Issue 3
DOI: 10.1063/1.1665613

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

Abstract

Citation Formats

Variational principles for natural divergence-free tensors in metric field theories journal, December 2012

Is the principle of least action a must? journal, March 2015

Minimal massive 3D gravity journal, July 2014

A Remarkable Property of the Riemann-Christoffel Tensor in Four Dimensions journal, October 1938

The Einstein Tensor and Its Generalizations journal, March 1971

Variational principles for natural divergence-free tensors in metric field theories
journal, December 2012

Is the principle of least action a must?
journal, March 2015

Minimal massive 3D gravity
journal, July 2014

A Remarkable Property of the Riemann-Christoffel Tensor in Four Dimensions
journal, October 1938

The Einstein Tensor and Its Generalizations
journal, March 1971