Vector boson scattering and boundary conditions in Kaluza-Klein toy model

We study a simple higher-dimensional toy model of electroweak symmetry breaking, in particular a pure gauge 5D theory on flat background with one extra finite space dimension. The principle of least action and the requirement of gauge independence of scattering amplitudes are used to determine the possible choices of boundary conditions. We demonstrate that for any of these choices the scattering amplitudes of vector bosons do not exhibit power-like growth in the high energy limit. Our analysis is an extension and generalization of the results obtained previously by other authors.