  Internal and Lorentz symmetries are necessarily linked when considering non
scalar condensates. Here I review vectorial type condensation due to a non zero
chemical potential associated to some of the global conserved charges of the
theory. The phase structure is very rich since three distinct phases exists
depending on the value assumed by one of the zero chemical potential vector
self interaction terms. In a certain limit of the couplings and for large
chemical potential the theory is not stable. This limit corresponds to a gauge
type limit often employed to economically describe the ordinary vector mesons
self interactions in QCD. Our analysis is relevant since it leads to a number
of physical applications not limited to strongly interacting theories at non
zero chemical potential.
