Effective Scalar Field Theory and Reduction of Couplings

Abstract

A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the possibility to go beyond the renormalizable ${\varphi }^4$ theory without losing its predictive power. It is shown that there is a minimal extension with just one additional free parameter (the mass scale of the effective theory expansion) and some of its properties are discussed.

Comments: 33 pages, latex file, no figures, 33 pages. Minor changes. Final version appeared in Physical Review D