  When the electroweak action is rewritten in terms of SU(2) gauge invariant
variables, the Higgs can be interpreted as a conformal metric factor. We show
that asymptotic flatness of the metric is required to avoid a Gribov problem:
without it, the new variables fail to be nonperturbatively gauge invariant. We
also clarify the relations between this approach and unitary gauge fixing, and
the existence of similar transformations in other gauge theories.
