Erratum: The renormalization group functions and the effective potential

It is first demonstrated how the effective potential Veff in a self-interacting scalar theory can be computed using operator regularization. We examine and theories, recovering the usual results in the former case and showing how Veff is a power series in the square root of the coupling λ in the latter. Scheme dependence of Veff is considered. Since no explicit divergences occur when one uses operator regularization, the renormalization group functions (β and γ) associated with the dependence of λ and on the radiatively induced scale parameter μ must be determined by considering the finite effective potential. It is shown that one must in fact compute Veff to a higher power in the perturbative expansion than if β and γ were to be computed using Green's functions. The usual results to lowest order are recovered in the model. Finally, a nonperturbative β function is determined by requiring that the mass generated by radiative effects be independent of μ2; it is found that both and are asymptoticly free with...