Catastrophe theoretic approach to the Higgs Mechanism

TL;DR

This paper applies Thom's Catastrophe Theory to analyze the Higgs Mechanism, revealing it as a first-order phase transition and suggesting alternative parameter regimes could have implications for physics beyond the Standard Model.

Contribution

It introduces a geometric, catastrophe-theoretic framework to understand the Higgs Mechanism as a discontinuous phase transition, expanding the conceptual landscape of symmetry breaking.

Findings

Higgs Mechanism arises as a first-order phase transition.

Different parameter choices can prevent the Higgs Mechanism.

Potential implications for beyond Standard Model physics.

Abstract

A geometric perspective of the Higgs Mechanism is presented. Using Thom's Catastrophe Theory, we study the emergence of the Higgs Mechanism as a discontinuous feature in a general family of Lagrangians obtained by varying its parameters. We show that the Lagrangian that exhibits the Higgs Mechanism arises as a first-order phase transition in this general family. We find that the Higgs Mechanism (as well as Spontaneous Symmetry Breaking) need not occur for a different choice of parameters of the Lagrangian, and further analysis of these unconventional parameter choices may yield interesting implications for beyond standard model physics.