A nonperturbative method for the Yang Mills Lagrangian

TL;DR

This paper introduces a nonperturbative approach to analyze the Yang Mills Lagrangian, deriving relations among renormalization constants and showing the beta function's structure aligns with the 't Hooft scheme.

Contribution

It presents a novel nonperturbative method leveraging the partition function to determine renormalization relations and the all-orders beta function form in Yang Mills theory.

Findings

All orders beta function contains only first two coefficients.

Relations among renormalization constants derived from the partition function.

Beta function matches the 't Hooft scheme structure.

Abstract

Using the properties of the partition function for a Yang Mills theory we compute simple relations among the renormalization constants. In the particular case of the background gauge field method we obtain that the all orders beta function for the gauge coupling constant contains only the first two orders coefficients different than zero and thus corresponds to the 't Hooft scheme.