  At sufficiently high chemical potential massive relativistic spin one fields
condense. This phenomenon leads to the spontaneous breaking of rotational
invariance while linking it to the breaking of internal symmetries. We study
the relevant features of the phase transition and the properties of the
generated Goldstone excitations. The interplay between the internal symmetry of
the vector fields and their Lorentz properties is studied. We predict that new
phases set in when vectors condense in Quantum Chromodynamics like theories.
