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. Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In mathematical formulations of quantum mechanics, an operator is a linear transformation from a Hilbert space to itself. ... In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical... Look up Vacuum in Wiktionary, the free dictionary For other uses, see vacuum (disambiguation) A vacuum is a volume of space that is empty of matter, including air, so that gaseous pressure is much less than standard atmospheric pressure. ... In 1948 Dutch physicist Hendrik B. G. Casimir of Philips Research Labs predicted that two uncharged parallel metal plates will be subject to a force pressing them together. ...

This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking. Examples are: In quantum field theory, correlation functions generalize the concept of correlation functions in statistics. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ...

• 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, G_μν, can only have a scalar expectation value such as . Higgs bosons are hypothetical elementary particles predicted to exist by the Standard Model of particle physics. ... A GEV (or Ground Effect Vehicle) is vehicle that takes advantage of the aerodynamic principle of ground effect (or Wing-in-ground). ... The Higgs mechanism, originally discovered by the British physicist Peter Higgs (building on a previous suggestion by Philip Anderson in condensed matter physics), is the mechanism that gives masses to all elementary particles in particle physics. ... This article or section should be merged with fermionic condensate In a theory with two chiral fields, ψ1 and ψ2 with a global symmetry relating the relative phases of both fields, but at low temperatures, the correlation function is nonzero, then we say a fermion condensate (also called chiral condensate... Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. ... In Quantum chromodynamics (QCD), the gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to certain hadrons. ... Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... The concept of a scalar is used in mathematics and physics. ... Charge is a word with many different meanings. ... In particle physics, fermions, (named after Enrico Fermi), are particles with semi-integer spin. ...

In some vacua of string theory, however, non-scalar condensates are found. If these describe our universe, then Lorentz symmetry violation may be observable. Look up Vacuum in Wiktionary, the free dictionary For other uses, see vacuum (disambiguation) A vacuum is a volume of space that is empty of matter, including air, so that gaseous pressure is much less than standard atmospheric pressure. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles... This article needs to be updated. ...

See also

• Wightman axioms and Correlation function (quantum field theory)
• vacuum energy or dark energy
• Spontaneous symmetry breaking

In physics the Wightman axioms are an attempt of mathematically stringent, axiomatic formulation of quantum field theory. ... In quantum field theory, correlation functions generalize the concept of correlation functions in statistics. ... It has been suggested that this article or section be merged with Zero-point energy. ... In cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ...