Vacuum expectation value
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 examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect.
- The Higgs field has a vacuum expectation value of 246 GeV  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.
- 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. 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 .
- Amsler, C.; Doser, M.; Antonelli, M.; Asner, D.; Babu, K.; Baer, H.; Band, H.; Barnett, R.; Bergren, E.; Beringer, J.; Bernardi, G.; Bertl, W.; Bichsel, H.; Biebel, O.; Bloch, P.; Blucher, E.; Blusk, S.; Cahn, R. N.; Carena, M.; Caso, C.; Ceccucci, A.; Chakraborty, D.; Chen, M. -C.; Chivukula, R. S.; Cowan, G.; Dahl, O.; d'Ambrosio, G.; Damour, T.; De Gouvêa, A.; Degrand, T. (2008). "Review of Particle Physics⁎". Physics Letters B. 667: 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. Archived from the original on 2012-07-12. Retrieved 2015-09-04.
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