Spontaneous symmetry breaking in a classical particle

TL;DR

This paper presents a pedagogical classical model demonstrating how gauge principles and spontaneous symmetry breaking can occur outside quantum systems, illustrating fundamental concepts relevant to phase transitions.

Contribution

It introduces a classical particle system as a model to illustrate gauge symmetry and spontaneous symmetry breaking, challenging the notion that these phenomena are exclusive to quantum systems.

Findings

Classical system can exhibit gauge symmetry breaking

Model illustrates phase transition concepts in a pedagogical way

Highlights relevance to various physical phenomena

Abstract

Due to the fact that only matter fields have phase, frequently is believed that the gauge principle can induce gauge fields only in quantum systems. But this is not necessary. This paper, of pedagogical scope, presents a classical system constituted by a particle in a classical potential, which is used as a model to illustrate the gauge principle and the spontaneous symmetry breaking. Those concepts appear in the study of second order phase transitions. Ferroelectricity, ferromagnetism, superconductivity, plasmons in a free electron gas, and the mass of vector bosons in the gauge field Yang-Mills theories, are some of the phenomena in which these transitions occur.