Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization

TL;DR

This paper extends a systematic renormalization method for Hamiltonian light-front field theory to include particle masses non-perturbatively, addressing a key limitation for applying the approach to realistic QCD calculations.

Contribution

It introduces a non-perturbative mass inclusion into the renormalization method, enhancing its applicability to full QCD beyond the massless approximation.

Findings

Identifies new challenges when including masses non-perturbatively.

Demonstrates the method using massive phi^3 theory in 5+1 dimensions.

Highlights differences in algebraic and conceptual complexity with masses.

Abstract

Hamiltonian light-front field theory can be used to solve for hadron states in QCD. To this end, a method has been developed for systematic renormalization of Hamiltonian light-front field theories, with the hope of applying the method to QCD. It assumed massless particles, so its immediate application to QCD is limited to gluon states or states where quark masses can be neglected. This paper builds on the previous work by including particle masses non-perturbatively, which is necessary for a full treatment of QCD. We show that several subtle new issues are encountered when including masses non-perturbatively. The method with masses is algebraically and conceptually more difficult; however, we focus on how the methods differ. We demonstrate the method using massive phi^3 theory in 5+1 dimensions, which has important similarities to QCD.