  Gauge theories formulated in a space-time manifold that includes compact
extra dimensions can show a nontrivial gauge structure. Depending on whether
the gauge parameters propagate or not in the extra dimensions, two different
Kaluza--Klein theories can arise when the extra dimensions are compactified. A
comparison between these two possibilities, in the context of a five
dimensional theory, is presented from both the theoretical and phenomenological
viewpoints. The phenomenological implications of these theories are contrasted
by discussing the one--loop decay of the Higgs boson into two photons. It is
shown that the amplitude for this decay differs substantially from one approach
to the other and that such a difference is intimately related to gauge
invariance.
