For articles related to the vacuum expectation value, see Quantum vacuum (disambiguation).
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In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by One of the most widely used 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. This value is given by , where MW is the mass of the W Boson, the reduced Fermi constant, and g the weak isospin coupling, in natural units. It is also near the limit of the most massive nuclei, at v = 264.3 Da.
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 charge.[citation needed] 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.[which?] If these describe our universe, then Lorentz symmetry violation may be observable.
^Amsler, C.; et al. (2008). "Review of Particle Physics⁎". Physics Letters B. 667 (1–5): 1–6. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. Archived from the original on 2012-07-12. Retrieved 2015-09-04.
and 21 Related for: Vacuum expectation value information
the vacuumexpectationvalue (also called condensate or simply VEV) of an operator is its average or expectationvalue in the vacuum. The vacuum expectation...
may have non-vanishing vacuumexpectationvalues called condensates. In the Standard Model, the non-zero vacuumexpectationvalue of the Higgs field, arising...
dielectrics, alter the vacuumexpectationvalue of the energy of the second-quantized electromagnetic field. Since the value of this energy depends on...
leaving the vacuum empty in the literal sense of the word. One important exception, however, is the vacuum energy or the vacuumexpectationvalue of the energy...
extremizing the effective action yields the equations of motion for the vacuumexpectationvalues of the quantum fields. The effective action also acts as a generating...
massless. At a critical temperature, the Higgs field develops a vacuumexpectationvalue; some theories suggest the symmetry is spontaneously broken by...
Decay to smaller vacuum expectationvalue, resulting in decrease of Casimir effect and destabilization of proton. Decay to vacuum with larger neutrino mass...
tensor is represented as Gμν, then the gluon condensate is the vacuumexpectationvalue ⟨ G μ ν G μ ν ⟩ {\displaystyle \langle G_{\mu \nu }G^{\mu \nu }\rangle...
\left(|h|^{2}-{\frac {v^{2}}{2}}\right)^{2}\ ,} where v {\displaystyle v} is the vacuumexpectationvalue. The L y {\displaystyle \ {\mathcal {L}}_{y}\ } term describes...
part of the interaction term which corresponds to the nonzero vacuumexpectationvalue of the Higgs field is moved from the interaction to the free field...
symmetry breaking, these fermions acquire a mass proportional to the vacuumexpectationvalue of the Higgs field. This Higgs-fermion coupling was first described...
This writes the vacuumexpectationvalue of a non-local operator as a sum over VEVs of local operators, i.e., condensates. The value of the correlation...
^{2}>0} , so that φ {\displaystyle \varphi } acquires a non-zero Vacuumexpectationvalue, which generates masses for the Electroweak gauge fields (the Higgs'...
thermal quantum field theory. It indicates confinement because its vacuumexpectationvalue must vanish in the confined phase due to its non-invariance under...
theory postulates that there is a vacuum state with very large vacuum energy, caused by a non-zero vacuumexpectationvalue of the inflaton field. Any region...
(often a background field) which acquires an expectationvalue (not necessarily a vacuumexpectationvalue) which is not invariant under the symmetry in...
field. Since the Higgs field vacuumexpectationvalue is nonzero, particles interact with this field all the time even in vacuum. This changes their weak...
Higgs vacuumexpectationvalue. The sum of squares of boson masses (that is, W, Z, and Higgs bosons) is also very close to half of squared Higgs vacuum expectation...