About gauge invariance in compactified extra dimensions

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.