Different Symmetry Realizations in Relativistic Coupled Bose Systems at Finite Temperature and Densities

We revisited the calculation of the effective potential for self-interacting scalar field with U (1) charge at one loop approximation. We show that high charge densities can induce important changes in the phase structure of the theory. A class of very interesting phenomena appear when we introduce finite density effects, e.g. symmetry nonrestoration, inverse symmetry breaking and anticipation of the high temperature symmetry restoration. The extension of these calculations in the context of multi-scalar field theory is outlined, with the objectives of studying the effects of a finite charge on the symmetry breaking phase transition, and to learn how these effects change the number of phases allowed by the system symmetries.