An effective potential that is real

In theories with spontaneous symmetry breaking, the exact effective potential V(${\mathrm{\phi }}_{\mathit{c}}$,T) is real, but its loop expansion can be complex. A generalization of the effective potential is developed that is real and that can be computed perturbatively. For the theory with the classical potential V(φ)=(λ/4)(${\mathrm{\phi }}^2$-${\mathrm{\sigma }}^2$ ${)}^2$, this real effective potential closely tracks the usual effective potential where the latter is real, ‖${\mathrm{\phi }}_{\mathit{c}}$‖≥σ/ √3 , and at finite temperatures displays at ${\mathrm{\phi }}_{\mathit{c}}$=0 a local minimum, which may have astrophysical implications. The critical temperature at the one-loop level runs from ${\mathit{T}}_{\mathit{C}}$≊1.81σ for λ=0.1 to ${\mathit{T}}_{\mathit{C}}$≊1.74σ for λ=1.