Compact fields and mass generation

TL;DR

This paper demonstrates that compact angular fields can acquire a nonzero propagator mass through a kinematical mechanism, as shown in an O(2) model with spontaneous symmetry breaking.

Contribution

It introduces the concept of kinematical mass generation for compact fields and calculates the massive propagator of the Goldstone boson in an O(2) model.

Findings

The free propagator of a compact field gains a nonzero mass.

The Goldstone boson propagator becomes massive due to the condensate.

Mass $oldsymbol{\omega}$ depends on the scalar condensate $ar{oldsymbol{\phi}}$.

Abstract

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' ${\bar\phi}$.