Elitzur's theorem Elitzur's theorem is a theorem in quantum and statistical field theory stating that in gauge theories with a compact gauge group, the only operators that can have non-vanishing expectation values are ones that are invariant under local gauge transformations. The direct implication of this is that local gauge symmetry cannot be spontaneously broken. The theorem was proposed in 1975 by Shmuel Elitzur, who proved it for Abelian gauge fields on a lattice. It is nonetheless possible to spontaneously break a global symmetry within a theory that has a local gauge symmetry, as in the Higgs mechanism.
Contents 1 See also 2 Notes 3 References 4 External links See also Mermin–Wagner theorem Notes ^ Fradkin, E. (2021). "18.6". Quantum Field Theory: An Integrated Approach. Princeton University Press. p. 533-534. ISBN 978-0691149080. ^ Elitzur S (1975). "Impossibility of spontaneously breaking local symmetries". Phys. Rev. D. 12: 3978–3982. Bibcode:1975PhRvD..12.3978E. doi:10.1103/PhysRevD.12.3978. References Itzykson, Claude; Drouffe, Jean-Michel (1989), Statistical field theory. Vol. 1, Cambridge Monographs on Mathematical Physics, Cambridge University Press, ISBN 978-0-521-34058-8, MR 1175176 External links Notes on lattice gauge theory by A. Muramatsu This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.
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