# Elitzur's theorem

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.[1] The theorem was proposed in 1975 by Shmuel Elitzur, who proved it for Abelian gauge fields on a lattice.[2] 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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