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. Because of 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.

• Received 15 January 2007

DOI:https://doi.org/10.1103/PhysRevD.75.105014