Conformal geometry: Difference between revisions
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{{Quantum field theory|cTopic=Tools}} | |||
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: | |||
*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}} |
Revision as of 20:07, 10 January 2014
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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 . 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 Higgs field has a vacuum expectation value of 246 GeV [1] 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 quarks, 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 scalars and have vanishing chargeTemplate:Fact. Thus fermion condensates must be of the form , where ψ is the fermion field. Similarly a tensor field, Gμν, can only have a scalar expectation value such as .
In some vacua of string theory, however, non-scalar condensates are foundTemplate:Which. If these describe our universe, then 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
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