Kaluza-Klein towers for real vector fields in flat space

We consider a free real vector field propagating in a five-dimensional flat space with its fifth dimension compactified either on a strip or on a circle and perform a Kaluza-Klein reduction which breaks SO(4,1) invariance while preserving SO(3,1) invariance. Taking into account the Lorenz gauge condition, we obtain from the most general Hermiticity conditions for the relevant operators all the allowed boundary conditions which have to be imposed on the fields in the extra dimension. The physical Kaluza-Klein mass towers, which result in a four-dimensional brane, are determined in the different distinct allowed cases. They depend on the bulk mass, on the parameters of the boundary conditions and on the extra parameter present in the Lagrangian. They involve vector states together, currently, with accompanying mass-shifted scalar states.