Solution to the non-perturbative renormalization of gauge theory

TL;DR

This paper presents a non-perturbative renormalization method for gauge theories within an effective light-cone Hamiltonian framework, offering new insights into the short-distance behavior of QCD and QED.

Contribution

It introduces a renormalization procedure that handles gauge theories non-perturbatively using cut-off functions and counter terms in a light-cone Hamiltonian approach.

Findings

Renormalization makes the Hamiltonian cut-off independent.

The approach reveals how cut-off functions influence the Coulomb potential.

Provides new physical insights into gauge theory potentials at short distances.

Abstract

The long standing problem of a non-perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. The approach provides new physical insight into the nature of gauge theory and the potential energy of QCD and QED at short distance.