The Nambu-Goldstone theorem in non-relativistic systems

TL;DR

This paper investigates the relationship between spontaneous symmetry breaking and Nambu-Goldstone bosons in non-relativistic systems, emphasizing the importance of operator methods to determine their dispersion relations.

Contribution

It introduces an operator-based approach to accurately derive the dispersion relations of Nambu-Goldstone bosons in non-relativistic contexts.

Findings

Number of Nambu-Goldstone bosons can be less than the number of broken generators.

Operator methods are effective in analyzing dispersion relations.

The relation between broken generators and Nambu-Goldstone bosons is more complex than in relativistic systems.

Abstract

In non-relativistic systems, when there is spontaneous symmetry breaking, the number of Nambu-Goldstone bosons ($n_{NG}$) are not necessarily equal to the number of broken generators ($n_{BG}$). Here we use the method of operators for analyzing the necessary conditions in order to obtain the correct dispersion relation for the Nambu-Goldstone bosons.