THE RENORMALIZATION-GROUP FUNCTIONS AND THE EFFECTIVE POTENTIAL (VOL 72, PG 250, 1994)

It is first demonstrated how the effective potential V-eff in a self-i nteracting scalar theory can be computed using operator regularization . We examine phi(4)(4) and phi(3)(6) theories, recovering the usual re sults in the former case and showing how V-eff is a power series in th e square root of the coupling lambda in the latter. Scheme dependence of V-eff is considered. Since no explicit divergences occur when one u ses operator regularization, the renormalization group functions (beta and gamma) associated with the dependence of lambda and phi on the ra diatively induced scale parameter mu must be determined by considering the finite effective potential. It is shown that one must in fact com pute V-eff to a higher power in the perturbative expansion than if bet a and gamma were to be computed using: Green's functions. The usual re sults to lowest order are recovered in the phi(4)(4) model. Finally, a nonperturbative beta function is determined by requiring that the mas s generated by radiative effects be independent of mu(2); it is found that both phi(4)(4) and phi(3)(6) are asymptoticly free with this beta function. In the appendix we explicitly compute a two-loop integral e ncountered in the evaluation of V-eff.