Physical stress, mass, and energy for nonrelativistic matter
For theories of relativistic matter fields there exist two possible definitions of the stressenergy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stressenergy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for nonrelativistic matter theories. We point out that while the physical nonrelativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. In conclusion, we also provide computations of these quantities for some simple nonrelativistic actions.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
 Cornell Univ., Ithaca, NY (United States). Cornell Lab. for Acceleratorbased Sciences and Education (CLASSE)
 Univ. of Chicago, Chicago, IL (United States). Kadanoff Center for Theoretical Physics
 Publication Date:
 Grant/Contract Number:
 FG0213ER41958; SC0009924
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of Chicago, IL (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; SpaceTime Symmetries; Differential and Algebraic Geometry; Effective Field Theories
 OSTI Identifier:
 1465514
Geracie, Michael, Prabhu, Kartik, and Roberts, Matthew M. Physical stress, mass, and energy for nonrelativistic matter. United States: N. p.,
Web. doi:10.1007/JHEP06(2017)089.
Geracie, Michael, Prabhu, Kartik, & Roberts, Matthew M. Physical stress, mass, and energy for nonrelativistic matter. United States. doi:10.1007/JHEP06(2017)089.
Geracie, Michael, Prabhu, Kartik, and Roberts, Matthew M. 2017.
"Physical stress, mass, and energy for nonrelativistic matter". United States.
doi:10.1007/JHEP06(2017)089. https://www.osti.gov/servlets/purl/1465514.
@article{osti_1465514,
title = {Physical stress, mass, and energy for nonrelativistic matter},
author = {Geracie, Michael and Prabhu, Kartik and Roberts, Matthew M.},
abstractNote = {For theories of relativistic matter fields there exist two possible definitions of the stressenergy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stressenergy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for nonrelativistic matter theories. We point out that while the physical nonrelativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. In conclusion, we also provide computations of these quantities for some simple nonrelativistic actions.},
doi = {10.1007/JHEP06(2017)089},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2017,
place = {United States},
year = {2017},
month = {6}
}