A More-effective Potential *

In theories with spontaneous symmetry breaking, the loop expansion of the effective potential is awkward. In such theories, the exact effective potential V (φc, T ) is real and convex (as a function of the classical field φc), but its perturbative series can be complex with a real part that is concave. These flaws limit the utility of the effective potential, particularly in studies of the early universe. A generalization of the effective potential is available that is real, that has no obvious convexity problems, and that can be computed in perturbation theory. For the theory with classical potential V (φ) = (λ/4)(φ2 − σ2)2, this more-effective potential closely tracks the usual effective potential where the latter is real |φc| ≥ σ/ √ 3 and naturally extends it to φc = 0, revealing that the critical temperature at the one-loop level runs from TC ≈ 1.81σ for λ = 0.1 to TC ≈ 1.74σ for λ = 1. This work was supported by the Director, Office of Energy Research, Office of High-Energy and Nuclear Physics, Division of High-Energy Physics of the U.S. Department of Energy under contracts DE-AC03-76SF00098 and DE-FG04-84ER40166. Permanent address, e-mail: [email protected]