Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation

TL;DR

This paper studies the asymptotic symmetries of scalar electrodynamics and the abelian Higgs model using Hamiltonian methods, revealing differences between massive and massless scalars and confirming Poincaré symmetry in the Higgs case.

Contribution

It extends previous analyses of electromagnetic asymptotic symmetries to include scalar fields and the Higgs model within the Hamiltonian framework.

Findings

Massless scalars do not support asymptotic boost symmetries.

Massive scalars and the Higgs model exhibit standard Poincaré symmetries.

The Hamiltonian formulation clarifies the structure of asymptotic symmetries.

Abstract

We investigate the asymptotic symmetry group of a scalar field minimally-coupled to an abelian gauge field using the Hamiltonian formulation. This extends previous work by Henneaux and Troessaert on the pure electromagnetic case. We deal with minimally coupled massive and massless scalar fields and find that they behave differently insofar as the latter do not allow for canonically implemented asymptotic boost symmetries. We also consider the abelian Higgs model and show that its asymptotic canonical symmetries reduce to the Poincar\'e group in an unproblematic fashion.