Spontaneous Breaking of Lorentz Invariance

TL;DR

This paper explores a mechanism where fermion interactions can spontaneously break Lorentz invariance by inducing a non-zero fermion number density in the vacuum, with implications for models involving composite gauge bosons and Lorentz violation signals.

Contribution

It introduces a stable effective theory demonstrating spontaneous Lorentz breaking via fermion density, linking it to models with composite gauge bosons and potential Lorentz violation signals.

Findings

Fermion attraction can lead to non-zero fermion density in vacuum.

Spontaneous Lorentz breaking can generate effective gauge bosons.

Potential observable signals of Lorentz violation in electrodynamics.

Abstract

We describe how a stable effective theory in which particles of the same fermion number attract may spontaneously break Lorentz invariance by giving non-zero fermion number density to the vacuum (and therefore dynamically generating a chemical potential term). This mecanism yields a finite vacuum expectation value $<\bar\psi\gamma^\mu\psi>$ which we consider in the context of proposed models that require such a breaking of Lorentz invariance in order to yield composite degrees of freedom that act approximately like gauge bosons. We also make general remarks about how the background source provided by $<\bar\psi\gamma^\mu\psi>$ could relate to work on signals of Lorentz violation in electrodynamics.