Phonons as Goldstone Bosons

TL;DR

This paper explores the analogy between phonons in solids and Goldstone bosons, highlighting how hidden symmetries lead to nonlinear phonon interactions similar to pion scattering.

Contribution

It offers a novel perspective on sound wave properties by linking them to spontaneously broken symmetries and Goldstone bosons, emphasizing the nonlinear nature of phonon equations.

Findings

Sound waves in solids are governed by nonlinear equations due to hidden symmetries.

Phonon-phonon scattering is analogous to pion-pion scattering in particle physics.

The analysis provides a symmetry-based understanding of phonon interactions.

Abstract

The implications of the hidden, spontaneously broken symmetry for the properties of the sound waves of a solid are analyzed. Although the discussion does not go beyond standard wisdom, it presents some of the known results from a different perspective. In particular, I argue that, as a consequence of the hidden symmetry, the equations of motion for a sound wave necessarily contain nonlinear terms, describing phonon-phonon scattering and emphasize the analogy with the low energy theorems for pion-pion scattering.