Spontaneous Breakdown of the Lorentz Invariance in Three-Dimensional Gauge Theories

TL;DR

This paper demonstrates that in certain three-dimensional abelian gauge theories, Lorentz invariance can spontaneously break due to dynamical magnetic field generation, leading to a ground state similar to the quantum Hall effect with a gapless photon acting as a Nambu-Goldstone boson.

Contribution

It provides a simple explanation and sufficient conditions for spontaneous Lorentz invariance breaking in 3D gauge theories, linking it to magnetic field generation and zero-point energy shifts.

Findings

Lorentz invariance is spontaneously broken by a dynamical magnetic field.

The ground state resembles the quantum Hall effect.

A topologically massive photon becomes gapless as a Nambu-Goldstone boson.

Abstract

In a class of renormalizable three-dimensional abelian gauge theory the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field $B$. The true ground state resembles that of the quantum Hall effect. An originally topologically massive photon becomes gapless, fulfilling the role of the Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance. We give a simple explanation and a sufficient condition for the spontaneous breaking of the Lorentz invariance with the aid of the Nambu-Goldstone theorem. The decrease of the energy density by $B \not= 0$ is understood mostly due to the shift in zero-point energy of photons. For PASCOS'94.