Elitzur's Theorem

Elitzur's Theorem, in quantum field theory and statistical field theory, states that in a gauge theory only operators invariant under local gauge transformations can have a non-vanishing expectation value, with the consequence that a local gauge symmetry can never be spontaneously broken. Proved in 1975 by Shmuel Elitzur within lattice field theory, and expected to hold in the continuum limit as well, the theorem shows that the ordinary picture of the Higgs mechanism as spontaneous symmetry breaking of a gauge symmetry is not literally correct, though the underlying physics can be reformulated entirely in terms of gauge invariant quantities.