  We investigate spontaneous symmetry breaking in Lorentz-noninvariant
theories. Our general discussion includes relativistic systems at finite
density as well as intrinsically nonrelativistic systems. The main result of
the paper is a direct proof that nonzero density of a non-Abelian charge in the
ground state implies the existence of a Goldstone boson with nonlinear
(typically, quadratic) dispersion law. We show that the Goldstone boson
dispersion relation may in general be extracted from the current transition
amplitude and demonstrate on examples from recent literature, how the
calculation of the dispersion relation is utilized by this method. After then,
we use the general results to analyze the nonrelativistic degenerate Fermi gas
of four fermion species. Due to its internal SU(4) symmetry, this system
provides an analog to relativistic two-color quantum chromodynamics with two
quark flavors. In the end, we extend our results to pseudo-Goldstone bosons of
an explicitly broken symmetry.
