DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

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. 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:
Research Org.:
Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1465514
Grant/Contract Number:  
FG02-13ER41958; SC0009924
Resource 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
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

Citation Formats

Geracie, Michael, Prabhu, Kartik, and Roberts, Matthew M. Physical stress, mass, and energy for non-relativistic matter. United States: N. p., 2017. 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. https://doi.org/10.1007/JHEP06(2017)089
Geracie, Michael, Prabhu, Kartik, and Roberts, Matthew M. Fri . "Physical stress, mass, and energy for non-relativistic matter". United States. https://doi.org/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 = {Fri Jun 16 00:00:00 EDT 2017},
month = {Fri Jun 16 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Field theory on Newton-Cartan backgrounds and symmetries of the Lifshitz vacuum
journal, August 2015

  • Hartong, Jelle; Kiritsis, Elias; Obers, Niels A.
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)006

Hall Viscosity and Electromagnetic Response
journal, February 2012


Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
journal, October 2015

  • Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
  • Journal of Mathematical Physics, Vol. 56, Issue 10
  • DOI: 10.1063/1.4932967

Canonically Covariant Formulation of Landau'S Newtonian Superfluid Dynamics
journal, April 1994


Fields and fluids on curved non-relativistic spacetimes
journal, August 2015

  • Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)042

Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry
journal, July 2015


Low-energy effective theory in the bulk for transport in a topological phase
journal, March 2015


Non-relativistic holography from Hořava gravity
journal, February 2013

  • Janiszewski, Stefan; Karch, Andreas
  • Journal of High Energy Physics, Vol. 2013, Issue 2
  • DOI: 10.1007/JHEP02(2013)123

Lifshitz space–times for Schrödinger holography
journal, June 2015


Hydrodynamics on the lowest Landau level
journal, June 2015


Viscoelastic response of topological tight-binding models in two and three dimensions
journal, October 2015


Non-relativistic scale anomalies
journal, June 2016

  • Arav, Igal; Chapman, Shira; Oz, Yaron
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)158

Weyl consistency conditions in non-relativistic quantum field theory
journal, December 2016

  • Pal, Sridip; Grinstein, Benjamín
  • Journal of High Energy Physics, Vol. 2016, Issue 12
  • DOI: 10.1007/JHEP12(2016)012

On the energy tensor of spinning massive matter in classical field theory and general relativity
journal, February 1976


Torsional Newton–Cartan geometry and the Schrödinger algebra
journal, June 2015


Boundary Effective Action for Quantum Hall States
journal, March 2016


Covariant effective action for a Galilean invariant quantum Hall system
journal, September 2016

  • Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)092

Aspects of hot Galilean field theory
journal, April 2015


Lifshitz scale anomalies
journal, February 2015

  • Arav, Igal; Chapman, Shira; Oz, Yaron
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)078

Effective Lagrangian and Topological Interactions in Supersolids
journal, May 2005


Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (Suite)
journal, January 1924

  • Cartan, Elie
  • Annales scientifiques de l'École normale supérieure, Vol. 41
  • DOI: 10.24033/asens.753

Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie)
journal, January 1923

  • Cartan, Elie
  • Annales scientifiques de l'École normale supérieure, Vol. 40
  • DOI: 10.24033/asens.751

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect
journal, January 2016

  • Golkar, Siavash; Nguyen, Dung X.; Son, Dam T.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)021

Theory of Thermal Transport Coefficients
journal, September 1964


Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography
journal, January 2014

  • Christensen, Morten H.; Hartong, Jelle; Obers, Niels A.
  • Journal of High Energy Physics, Vol. 2014, Issue 1
  • DOI: 10.1007/JHEP01(2014)057

Hydrodynamic Relations in Superconductivity
journal, August 1989


Nonrelativistic particles and wave equations
journal, December 1967

  • Lévy-Leblond, Jean-Marc
  • Communications in Mathematical Physics, Vol. 6, Issue 4
  • DOI: 10.1007/BF01646020

Anomalous breaking of anisotropic scaling symmetry in the quantum lifshitz model
journal, July 2012

  • Baggio, Marco; de Boer, Jan; Holsheimer, Kristian
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)099

Works referencing / citing this record:

Covariant Poisson’s equation in torsional Newton-Cartan gravity
journal, April 2019

  • Abedini, Mohammad; Afshar, Hamid R.; Ghodsi, Ahmad
  • Journal of High Energy Physics, Vol. 2019, Issue 4
  • DOI: 10.1007/jhep04(2019)117

Newton-Cartan gravity and torsion
journal, October 2017

  • Bergshoeff, Eric; Chatzistavrakidis, Athanasios; Romano, Luca
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/jhep10(2017)194

Covariant Poisson's equation in torsional Newton-Cartan gravity
text, January 2019