MS 4 : An Alternative to the Bogolyubov–Parasiuk–Hepp–Zimmermann (BPHZ) Theory

In this paper, we study the MS4 scheme of UV renormalization suggested during the formalization of considerations that produced a number of important algorithms in the past. Guaranteeing the finiteness of renormalized integrals by construction, MS4 satisfies the Bogolyubov axioms of the R-operation and is the 4-dimensional analog of the MS-scheme of ‘t Hooft. The well-known IBP algorithm is ported in MS4 with modifications, but without much difficulty. Features of the MS4 scheme: structure transparency, simplicity of arithmetic at $$D = 4$$ , and a spectrum of computing options. The direct derivation of RG equations operates only with explicitly finite quantities and immediately leads to expressions for RG functions in terms of explicit finite integrals of a special form.