World Library  
Flag as Inappropriate
Email this Article

Vacuum expectation value

Article Id: WHEBN0000296060
Reproduction Date:

Title: Vacuum expectation value  
Author: World Heritage Encyclopedia
Language: English
Subject: Vacuum state, Propagator, Quantum field theory, Wightman axioms, Casimir effect
Collection: Quantum Field Theory, Standard Model
Publisher: World Heritage Encyclopedia

Vacuum expectation value

In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. One of the most widely used, but controversial, examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect.

This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking. Examples are:

The observed Lorentz invariance of space-time allows only the formation of condensates which are Lorentz scalars and have vanishing charge. Thus fermion condensates must be of the form \langle\overline\psi\psi\rangle, where ψ is the fermion field. Similarly a tensor field, Gμν, can only have a scalar expectation value such as \langle G_{\mu\nu}G^{\mu\nu}\rangle.

In some vacua of string theory, however, non-scalar condensates are found. If these describe our universe, then Lorentz symmetry violation may be observable.

See also


  1. ^ Amsler, C.; Doser, M.; Antonelli, M.; Asner, D.; Babu, K.; Baer, H.; Band, H.; Barnett, R.; Bergren, E.; Beringer, J.; Bernardi, G.; Bertl, W.; Bichsel, H.; Biebel, O.; Bloch, P.; Blucher, E.; Blusk, S.; Cahn, R. N.; Carena, M.; Caso, C.; Ceccucci, A.; Chakraborty, D.; Chen, M. -C.; Chivukula, R. S.; Cowan, G.; Dahl, O.; d'Ambrosio, G.; Damour, T.; De Gouvêa, A.; Degrand, T. (2008). "Review of Particle Physics⁎". Physics Letters B 667: 1.  

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, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for 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.