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 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.