Compact fields and mass generation

It is shown that the free propagator of an angular, i.e. compact, field with zero lagrangian mass acquires a nonzero propagator mass $\omega$ (`kinematical' mass generation). To demonstrate this effect the free propagator of the goldstone boson in an O(2) model with spontaneous symmetry breaking is calculated. It is shown that this propagator is massive, the mass $\omega$ being a function of the scalar `condensate' ${\bar\phi}$.