Understanding of the Renormalization Program in a mathematically Rigorous Framework and an Intrinsic Mass Scale

TL;DR

This paper establishes a mathematically rigorous framework for the renormalization program using non-local field theories with an intrinsic mass scale, providing a finite perturbative approach and methods to estimate and bound this scale.

Contribution

It introduces a consistent, rigorous framework for renormalization using non-local theories with a finite mass scale, bridging to traditional methods.

Findings

A finite, rigorous perturbation program consistent with traditional renormalization.

A method to estimate the intrinsic mass scale (5).

A way to bound the mass scale (5) using the finite perturbation differences.

Abstract

we show there exists a mathematically consistent framework in which the Renormalization Program can be understood in a natural manner. The framework does not require any violations of mathematical rigor usually associated with the Renormalization program. We use the framework of the non-local field theories [these carry a finite mass scale (\Lambda)]and set up a finite perturbative program. We show how this program leads to the perturbation series of the usual renormalization program [except one difference] if the series is restructured .We further show that the comparison becomes possible if there exists a finite mass scale (\Lambda), with certain properties, in the Quantum Field theory [which we take to be the scale present in the nonlocal theory]. We give a way to estimate the scale (\Lambda). We also show that the finite perturbation program differs from the usual renormalization program by a term; which we propose can also be used to put a bound on (\Lambda).