# 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:

- Publication Date:

- 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.
```

```
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
```

```
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.
```

```
@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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https://doi.org/10.1016/j.physletb.2019.02.005

https://doi.org/10.1016/j.physletb.2019.02.005

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Cited by: 3 works

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