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Title: Physical stress, mass, and energy for non-relativistic matter

For theories of relativistic matter fields there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy 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 non-relativistic matter theories. We point out that while the physical non-relativistic 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 non-relativistic actions.
Authors:
 [1] ;  [2] ;  [3]
  1. Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
  2. Cornell Univ., Ithaca, NY (United States). Cornell Lab. for Accelerator-based Sciences and Education (CLASSE)
  3. Univ. of Chicago, Chicago, IL (United States). Kadanoff Center for Theoretical Physics
Publication Date:
Grant/Contract Number:
FG02-13ER41958; 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 1029-8479
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; Space-Time 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 non-relativistic 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 non-relativistic matter. United States. doi:10.1007/JHEP06(2017)089.
Geracie, Michael, Prabhu, Kartik, and Roberts, Matthew M. 2017. "Physical stress, mass, and energy for non-relativistic 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 non-relativistic 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 stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy 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 non-relativistic matter theories. We point out that while the physical non-relativistic 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 non-relativistic 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}
}