Kaluza-Klein towers for spinors in flat space

Considering a massive or massless free spinor field propagating in a flat five-dimensional space with its fifth dimension compactified either on a strip or on a circle, we analyze the procedure of generation of the four-dimensional Kaluza-Klein spinor mass towers. Requiring the five-dimensional Dirac operator to be symmetric, the set of all the allowed boundary conditions is obtained. In the determination of the boundary conditions and in the Kaluza-Klein reduction equations, the SO(3,1) and parity invariances in the space-time subspace are carefully taken into account. The equations determining the mass towers are written in full generality. A few numerical examples are given.