Renormalization group for the internal space

TL;DR

This paper introduces a novel renormalization group approach that orders fluctuations by their amplitude in an internal space, providing a functional equation that generalizes the Callan-Symanzik equation and resums loop expansions.

Contribution

It presents a new renormalization group method based on internal space parameters, differing from traditional external space approaches, and derives a functional differential equation.

Findings

Provides a new RG equation based on internal amplitude space

Generalizes the Callan-Symanzik equation

Resums loop expansion in a novel way

Abstract

The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated in a successive manner, as well, but their order is given by an internal space parameter, their amplitude. The differential version of the renormalization group equation is given which is the functional generalization of the Callan-Symanzik equation in one special case and resums the loop expansion in another one.