Englert-Brout-Higgs Mechanism in Nonrelativistic Systems

TL;DR

This paper explores the Englert-Brout-Higgs mechanism in nonrelativistic systems without Lorentz invariance, revealing how gauging non-Abelian symmetries affects spatial rotation and the spectrum of excitations.

Contribution

It extends the understanding of the Higgs mechanism to nonrelativistic contexts, analyzing effects of charge expectation values and background neutrality on symmetry breaking.

Findings

Gauging non-Abelian symmetries breaks spatial rotation in nonrelativistic systems.

Charge neutrality conditions influence the decoupling of background dynamics.

The spectrum remains continuous as gauge coupling approaches zero.

Abstract

We study the general theory of Englert-Brout-Higgs mechanism without assuming Lorentz invariance. In the presence of a finite expectation value of non-Abelian matter charges, gauging those symmetries always results in spontaneous breaking of spatial rotation. If we impose the charge neutrality by assuming a background with the opposite charges, the dynamics of the background cannot be decoupled and has to be fully taken into account. In either case, the spectrum is continuous as the gauge coupling is switched off.