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.
Facts
StatementIn a gauge theory, only operators that are invariant under local gauge transformations can have a non-vanishing expectation value, so a local gauge symmetry can never be spontaneously broken. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Elitzur's theorem, Wikipedia
Lead section
In gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant under local gauge transformations.
History section
The theorem was first proved in 1975 by Shmuel Elitzur in lattice field theory.
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