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

  • Michael Geracie
  • Kartik Prabhu
  • Matthew M. Roberts
Open Access
Regular Article - Theoretical Physics

Abstract

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. We also provide computations of these quantities for some simple non-relativistic actions.

Keywords

Space-Time Symmetries Differential and Algebraic Geometry Effective Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Michael Geracie
    • 1
  • Kartik Prabhu
    • 2
  • Matthew M. Roberts
    • 3
  1. 1.Center for Quantum Mathematics and Physics (QMAP), Department of PhysicsUniversity of CaliforniaDavisU.S.A.
  2. 2.Cornell Laboratory for Accelerator-based Sciences and Education (CLASSE)Cornell UniversityIthacaU.S.A.
  3. 3.Kadanoff Center for Theoretical PhysicsUniversity of ChicagoChicagoU.S.A.

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