THE RENORMALIZATION GROUP IMPROVED EFFECTIVE POTENTIAL IN MASSLESS MODELS

The effective potential V is considered in massless $\lambda\phi^4_4$ theory. The expansion of V in powers of the coupling λ and of the logarithm of the background field ϕ is reorganized in two ways; first as a series in λ alone, then as a series in lnϕ alone. By applying the renormalization group (RG) equation to V, these expansions can be summed. Using the condition V′(v)=0 (where v is the vacuum expectation value of ϕ) in conjunction with the expansion of V in powers of lnϕ fixes V provided v≠0. In this case, the dependence of V on ϕ drops out and V is not analytic in λ. Massless scalar electrodynamics is considered using the same approach.