  In this paper a model in a space-time with compact extra dimension is
presented, describing five-dimensional fermion fields interacting with an
electromagnetic field localized on a brane. This model can be considered as a
toy model for examining possible consequences of the localization of gauge
fields on a brane. It is shown that in the limit of infinite extra dimension,
the lowest-order amplitudes of some processes in the resulting four-dimensional
effective theory are divergent. Such a "localization catastrophe" can be
inherent to more realistic brane world models with infinite extra dimensions.
