Vacuum and Symmetry Breaking: New Approach

TL;DR

This paper introduces a novel symmetry breaking mechanism that incorporates topological degrees of freedom into Yang-Mills-Higgs theories, providing new insights especially for non-Abelian gauge theories.

Contribution

It presents a new field decomposition method that preserves classical dynamics and reveals topological degrees of freedom during symmetry breaking in non-Abelian theories.

Findings

Topological degrees of freedom emerge in non-Abelian symmetry breaking.

The method reproduces the Higgs mechanism in Abelian theories.

A new vacuum definition is proposed for analyzing the results.

Abstract

We propose a new mechanism for symmetry breaking in which, apart from particle degrees of freedom, topological degrees of freedom also emerge. In this method, a decomposition for the fields of the Yang-Mills-Higgs theory is introduced and Lagrangian is written based on new variables. This new Lagrangian does not change the dynamics of the theory, at least at the classical level. We study the spontaneous symmetry breaking for this new Lagrangian and show that how it works in Abelian and non-Abelian gauge theories. In the case of Abelian gauge theory our method adds nothing new to the so-called Higgs mechanism. However, in the non-Abelian case topological degrees of freedom, as classical fields, arise. Finally, we reacquire our results considering a new definition for the vacuum.