Scheme independence as an inherent redundancy in quantum field theory

TL;DR

This paper explores how scheme independence in quantum field theory can be understood as a redundancy arising from field redefinitions within the path integral framework, connecting it to the structure of exact renormalization group equations.

Contribution

It demonstrates that scheme independence is an inherent redundancy in quantum field theory, represented as a vector field transformation of the RG kernel under field redefinitions.

Findings

Exact renormalization group equations are a special case of Schwinger-Dyson-like relations.

Scheme independence corresponds to a vector field transformation of the RG kernel.

Path integral relations encode an infinite set of local identities.

Abstract

The path integral formulation of Quantum Field Theory implies an infinite set of local, Schwinger-Dyson-like relations. Exact renormalization group equations can be cast as a particular instance of these relations. Furthermore, exact scheme independence is turned into a vector field transformation of the kernel of the exact renormalization group equation under field redefinitions.