Vacuum expectation value
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In quantum field theory the vacuum expectation value (also called condensate) 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 best known examples of the vacuum expectation value of an operator leading to a physical effect 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. This nonzero value allows the Higgs mechanism to work.
- The chiral condensate in Quantum chromodynamics gives a large effective mass to quarks, and distinguishes between phases of quark matter.
- The gluon condensate in Quantum chromodynamics may 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 charge. 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 found. If these describe our universe, then Lorentz symmetry violation may be observable.
[edit] See also
- Wightman axioms and Correlation function (quantum field theory)
- vacuum energy or dark energy
- Spontaneous symmetry breaking
| Quantum field theory |
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| Field theory • overview of QFT • gauge theory • quantization • renormalization • partition function • vacuum state • anomaly • spontaneous symmetry breaking • condensates Some models: |
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