Bose-Einstein condensation, spontaneous symmetry breaking, and gauge theories

Bosonic chemical potentials for a variety of relativistic field theories are introduced via the methods of functional integrals with the aim of studying the relationship between Bose-Einstein condensation and spontaneous symmetry breaking. The models studied include the noninteracting and the self-interacting charged scalar field, scalar electrodynamics and the Higgs model, and the Weinberg-Salam model. In general the chemical potential acts as an effective symmetry-breaking parameter although the phase diagrams for the two cases ($m^2<0\mathrm{}$ and $m^2>0\mathrm{}$) look very different. It is found that the symmetry-restoring temperature in the Weinberg-Salam model increases with increasing electric charge density. Finally, the analysis of Jakobsen, Kon, and Segal of a conserved isotropic total angular momentum for the cosmic background radiation is shown to be erroneous.