Elitzur's theorem stating the impossibility of spontaneous breaking of
local symmetries in a gauge theory is reexamined. The existing proofs of
this theorem rely on gauge invariance as well as positivity of the weight
in the Euclidean partition function. We examine the validity of Elitzur's
theorem in gauge theories for which the Euclidean measure of the partition
function is not positive definite. We find that Elitzur's theorem does not
follow from gauge invariance alone. We formulate a general criterion under
which spontaneous breaking of local symmetries in a gauge theory is
excluded. Finally we illustrate the results in an exactly solvable two
dimensional abelian gauge theory.

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