Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes

TL;DR

This paper develops an algebraic and group theoretical framework for exponential renormalization in quantum field theory, focusing on Bogoliubov's R-operation and momentum subtraction schemes, with implications for classifying subtraction methods.

Contribution

It introduces a Hopf algebraic formulation of Bogoliubov's R-operation and provides an algebraic classification of subtraction schemes in renormalization.

Findings

Hopf algebraic formulation of R-operation

Classification of subtraction schemes

Insights into Taylor jet expansions in renormalization

Abstract

This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic and group theoretical approach to renormalisation. In particular, we describe in detail a Hopf algebraic formulation of Bogoliubov's classical R-operation and counterterm recursion in the context of momentum subtraction schemes. This approach allows us to propose an algebraic classification of different subtraction schemes. Our results shed light on the peculiar algebraic role played by the degrees of Taylor jet expansions, especially the notion of minimal subtraction and oversubtractions.