A renormalization group approach to Hamiltonian light-front field theory

TL;DR

This paper develops a perturbative renormalization group framework for Hamiltonian light-front field theory, addressing covariance issues and proposing a method to restore Lorentz invariance and cluster decomposition.

Contribution

It introduces a renormalization group approach using invariant-mass cutoffs and coupling coherence to improve light-front quantum field theory.

Findings

Invariant-mass cutoffs violate covariance but can be managed.

Coupling coherence helps restore Lorentz invariance.

Framework aims to facilitate practical renormalization in light-front QCD.

Abstract

A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by dropping irrelevant operators and using perturbation theory near Gaussian fixed volumes, employ invariant-mass cutoffs. These cutoffs violate covariance and cluster decomposition, and allow functions of longitudinal momenta to appear in all relevant, marginal, and irrelevant operators. These functions can be determined by insisting that the Hamiltonian display a coupling constant coherence, with the number of couplings that explicitly run with the cutoff scale being limited and all other couplings depending on this scale only through perturbative dependence on the running couplings. Examples are given that show how coupling coherence restores Lorentz covariance and cluster decomposition, as recently speculated by Wilson and the author. The ultimate goal of this work is a practical Lorentz metric version of the renormalization group, and practical renormalization techniques for light-front quantum chromodynamics.