An alternative to perturbative renormalization in 3+1 dimensional field theories

Abstract

Perturbative renormalization provides the bedrock of understanding quantum field theories. In this work, I point out an alternative way of renormalizing quantum field theories, which is naturally encountered and well known for the case of large N scalar field theories. In terms of bare parameters, this non-perturbative alternative renormalization differs qualitatively from its perturbative cousin: in the continuum limit, the bare coupling constant goes to zero instead of infinity, and there is no wave-function counterterm. Despite these differences, the resulting n-point functions of the theory are finite. I provide explicit results for alternative renormalization for the O(N) model and QCD with $N_f=12$ flavors in 3+1 dimensions.

Comments: 33 pages, no figures; v2: major revisions in subsection II.D to accommodate log(epsilon) terms, new appendix A, no qualitative changes; v3: fixed typos in appendix A (thanks, Willie!); v4: more typos fixed, additional comments, corresponds to journal version