Remarks on nonrelativistic Goldstone bosons

TL;DR

This paper explores the properties of Goldstone bosons in nonrelativistic systems, revealing the existence of gapped partners called almost-Goldstone bosons and linking dispersion deviations to time-reversal symmetry breaking.

Contribution

It introduces the concept of almost-Goldstone bosons as gapped partners to Type B Goldstone bosons and relates dispersion law deviations to symmetry breaking signatures.

Findings

Type B Goldstone bosons can have gapped partners.

Total count of Goldstone and almost-Goldstone bosons equals broken generators.

Dispersion deviations indicate small time-reversal symmetry breaking.

Abstract

We discuss excitations in nonrelativistic field theories with spontaneous breaking of a continuous global symmetry. It is known that in such systems there are two types of Goldstone bosons (Type A and Type B) whose dispersion law is generically linear or quadratic, respectively. We show that Type B Goldstone bosons may have gapped partners which we call almost-Goldstone bosons. With some nondegeneracy assumption about the low-energy effective action, the total number of Goldstone and almost-Goldstone bosons adds up to the number of broken symmetry generators. We propose that deviations of the dispersion law of Goldstone bosons from linearity at small momenta may serve as a signature of small breaking of time-reversal symmetry.