Spontaneous breaking of Lorentz invariance

We describe how a stable effective theory in which particles of the same fermion number attract may spontaneously break Lorentz invariance by giving a nonzero fermion number density to the vacuum (and therefore dynamically generating a chemical potential term). This mechanism yields a finite vacuum expectation value 〈ψ̅ γ^μψ〉, 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 〈ψ̅ γ^μψ〉 could relate to work on signals of Lorentz violation in electrodynamics.