MS4: a BPHZ killer

TL;DR

The paper introduces MS4, a four-dimensional renormalization scheme that simplifies calculations, ensures finiteness, and aligns with established theoretical principles, enhancing the efficiency of quantum field theory computations.

Contribution

It presents MS4 as a novel 4D renormalization scheme that guarantees finiteness, maintains causality, and improves computational transparency compared to previous methods.

Findings

MS4 guarantees finiteness of integrals by construction.

MS4 aligns with the Stueckelberg-Bogolyubov causality axiom.

RG equations can be derived using explicitly finite quantities.

Abstract

The UV renormalization scheme $\text{MS}^4$ emerged in the formalization of the reasoning which yielded an array of important algorithms in the 80's. $\text{MS}^4$ guarantees finiteness of renormalized integrals by construction, satisfies the Stueckelberg-Bogolyubov causality axiom for the R-operation, and turns out to be a 4-dimensional analog of t'Hooft's MS-scheme. The well-known IBP reduction algorithm can be ported to $\text{MS}^4$ with modifications, but without problems. $\text{MS}^4$ exhibits transparency of the structure, simplicity of the arithmetic at $D=4$, and new calculational options. A straightforward derivation of RG equations runs in terms of explicitly finite quantities and expresses RG functions in terms of explicitly finite integrals.