Operator regularization and the renormalization group to two-loop order in φ63

Abstract

Operator regularization is used to compute the renormalization group functions β(λ), γ m ( λ), and γ Γ ( λ) to two-loop order in φ 6 3 theory. At no stage in the computation do we encounter divergent quantities (even when the regulating parameter approaches its limiting value). These renormalization group functions are fully determined by the appropriate finite Green functions. We also show that, if minimal subtraction is used in conjunction with dimensional regularization, the renormalization group functions can be calculated either by considering the divergent counter terms (as is usually done) or by considering the appropriate finite Green functions (as in operator regularization).