Asymptotic Symmetries of SU(2) Yang-Mills-Higgs Theory in Hamiltonian Formulation

TL;DR

This paper analyzes the asymptotic symmetry group of SU(2) Yang-Mills-Higgs theory in the Hamiltonian framework, extending previous electromagnetism studies and addressing global charge conditions and boost symmetry implementations.

Contribution

It extends the understanding of asymptotic symmetries to SU(2) Yang-Mills-Higgs theory within the Hamiltonian formulation, including detailed analysis of charge and boost symmetry conditions.

Findings

No obstructions to global electric and magnetic charges.

Subtlety in magnetic charge case due to fall-off and parity conditions.

Hamiltonian boost symmetries require careful treatment.

Abstract

We investigate the asymptotic symmetry group of a SU(2)-Yang-Mills theory coupled to a Higgs field in the Hamiltonian formulation. This extends previous work on the asymptotic structure of pure electromagnetism by Henneaux and Troessaert, and on electromagnetism coupled to scalar fields and pure Yang-Mills fields by Tanzi and Giulini. We find that there are no obstructions to global electric and magnetic charges, though that is rather subtle in the magnetic case. Again it is the Hamiltionian implementation of boost symmetries that need a careful and technically subtle discussion of fall-off and parity conditions of all fields involved.