World Library  
Flag as Inappropriate
Email this Article

Local symmetry

Article Id: WHEBN0003655316
Reproduction Date:

Title: Local symmetry  
Author: World Heritage Encyclopedia
Language: English
Subject: Gauge theory, Standard Model (mathematical formulation), Lorentz covariance, Ramond–Ramond field, Supergravity
Collection: Symmetry
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Local symmetry

In physics, a local symmetry is symmetry of some physical quantity, which smoothly depends on the point of the base manifold. Such quantities can be for example an observable, a tensor or the Lagrangian of a theory. If a symmetry is local in this sense, then one can apply a local transformation (resp. local gauge transformation), which means that the representation of the symmetry group is a function of the manifold and can thus be taken to act differently on different points of spacetime.

The diffeomorphism group is a local symmetry and thus every geometrical or generally covariant theory (i.e. a theory whose equations are tensor equations, for example general relativity) has local symmetries.

Often the term local symmetry is specifically associated with local gauge symmetries in Yang–Mills theory (see also standard model) where the Lagrangian is locally symmetric under some compact Lie group. Local gauge symmetries always come together with some bosonic gauge fields, like the photon or gluon field, which induce a force in addition to requiring conservation laws.[1]

Examples

See also

References

  1. ^ Kaku, Michio (1993). Quantum Field Theory: A Modern Introduction. New York: Oxford University Press.  
  2. ^ Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973-09-15). "Gravitation". San Francisco: W. H. Freeman.  


This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.