Renormalization of Tamm-Dancoff Integral Equations

TL;DR

This paper presents a non-perturbative renormalization method for light-front Tamm-Dancoff equations, enabling cutoff-independent solutions for relativistic bound states in theories like QCD.

Contribution

It introduces a novel counterterm equation approach and a Rayleigh-Ritz numerical method for renormalization in light-front field theories.

Findings

Successfully applied to ultraviolet divergent models

Generated cutoff-independent bound state solutions

Derived counterterms using the Rayleigh-Ritz method

Abstract

During the last few years, interest has arisen in using light-front Tamm-Dancoff field theory to describe relativistic bound states for theories such as QCD. Unfortunately, difficult renormalization problems stand in the way. We introduce a general, non-perturbative approach to renormalization that is well suited for the ultraviolet and, presumably, the infrared divergences found in these systems. We reexpress the renormalization problem in terms of a set of coupled inhomogeneous integral equations, the ``counterterm equation.'' The solution of this equation provides a kernel for the Tamm-Dancoff integral equations which generates states that are independent of any cutoffs. We also introduce a Rayleigh-Ritz approach to numerical solution of the counterterm equation. Using our approach to renormalization, we examine several ultraviolet divergent models. Finally, we use the Rayleigh-Ritz approach to find the counterterms in terms of allowed operators of a theory.