Conformal geometry: Difference between revisions

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{{Quantum field theory|cTopic=Tools}}
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In [[quantum field theory]] the '''vacuum expectation value''' (also called '''condensate''' or simply VEV) of an [[Operator (physics)|operator]] is its average, [[Expectation value (quantum mechanics)|expected value]] in the [[Vacuum state|vacuum]]. The vacuum expectation value of an operator <var>O</var> is usually denoted by <math>\langle O\rangle</math>. 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 function (quantum field theory)|correlation functions]] in [[quantum field theory]]. It is also important in [[spontaneous symmetry breaking]]. Examples are:
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*The [[Higgs field]] has a vacuum expectation value of 246 [[GeV]] <ref>{{cite doi|10.1016/j.physletb.2008.07.018|noedit}}</ref> This nonzero value underlies the [[Higgs mechanism]] of the [[Standard Model]].
*The [[chiral condensate]] in [[Quantum chromodynamics]], about a factor of a thousand smaller than the above, gives a large effective mass to [[quark]]s, and distinguishes between phases of [[quark matter]]. This underlies the bulk of the mass of most hadrons.
*The [[gluon condensate]] in [[Quantum chromodynamics]] may also be partly responsible for masses of hadrons.
 
The observed [[Lorentz invariance]] of space-time allows only the formation of condensates which are [[Lorentz scalar]]s and have vanishing [[charge (physics)|charge]]{{fact|date=April 2013}}. Thus [[fermion]] condensates must be of the form <math>\langle\overline\psi\psi\rangle</math>, where <var>ψ</var> is the fermion field. Similarly a tensor field, <var>G</var><sub><var>μν</var></sub>, can only have a scalar expectation value such as <math>\langle G_{\mu\nu}G^{\mu\nu}\rangle</math>.
 
In some [[Vacuum#The quantum-mechanical vacuum|vacua]] of [[string theory]], however, non-scalar condensates are found{{which|date=April 2013}}. If these describe our [[universe]], then [[Lorentz_symmetry#Lorentz_violation|Lorentz symmetry violation]] may be observable.
 
==See also==
*[[Wightman axioms]] and [[Correlation function (quantum field theory)]]
*[[vacuum energy]] or [[dark energy]]
*[[Spontaneous symmetry breaking]]
 
== References ==
{{Reflist}}
 
{{DEFAULTSORT:Vacuum Expectation Value}}
[[Category:Quantum field theory]]
[[Category:Standard Model]]
 
{{Quantum-stub}}

Latest revision as of 03:12, 8 December 2014

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