The breaking of the SO(p, q) symmetry group to SO(p, q − n) × O(n) subjected to boundary conditions and its physical consequences for a gauge field theory

Abstract

The consequences of imposing boundary conditions to extra spacetime coordinates on a gauge field theory are considered. In a toy model, a larger spacetime symmetry described by a Lorentz-Poincaré SO(p, q) group is broken to a symmetry group of the form due to boundary conditions in the extra dimensions, leading to an effectively massive gauge field coupled to a “scalar” field in the observable spacetime coordinates.