Effective Potential Improvements, ǫ-expansions, and the Electroweak Phase Transition

Recently, there has been considerable interest in the “electroweak phase transition” (the temperature induced symmetry-changing phase transition[1] of the standard electroweak model), especially in connection with the possibility of dynamical generation of the baryon asymmetry. An appropriate tool for the investigation of this type of phenomena is the finite temperature effective action[2] ΓT (φ(x)), where φ(x) is a trial vacuum expectation value of a scalar quantum field of the theory. ΓT (φ(x)) is the generating functional of the one-particle irreducible Green’s functions, and therefore encodes all physical information about the theory, but unfortunately, its evaluation is extremely difficult. An important simplification can be achieved by considering position independent trial vacuum expectation values, φ(x)=constant=φ. This leads to the introduction of the finite temperature effective potential VT (φ), which is related to ΓT (φ(x)) by