A Simple Proof of the BPH Theorem

TL;DR

This paper presents a new formalism for renormalization in quantum field theories that simplifies the proof of the BPH theorem and has broad applications in various renormalization contexts.

Contribution

It introduces a formalism with no overlapping divergences and provides a straightforward proof of the BPH theorem, enhancing understanding of renormalization procedures.

Findings

Formalism eliminates overlapping divergences

Proof of BPH theorem within the new framework

Applications to lattice perturbation theory and operator product expansion

Abstract

A new formalism is given for the renormalization of quantum field theories to all orders of perturbation theory, in which there are manifestly no overlapping divergences. We prove the BPH theorem in this formalism, and show how the local subtractions add up to counterterms in the action. Applications include the renormalization of lattice perturbation theory, the decoupling theorem, Zimmermann oversubtraction, the renormalization of operator insertions, and the operator product expansion.