Systematic Renormalization in Hamiltonian Light-Front Field Theory

TL;DR

This paper introduces a systematic method for renormalizing Hamiltonian light-front field theories, ensuring rapid convergence of bound state calculations without dropping Fock sectors, and applies it to phi-cubed theory as a demonstration.

Contribution

The authors develop a unique renormalization approach that maintains all Fock sectors and respects physical principles, applicable to QCD and demonstrated on phi-cubed theory.

Findings

Hamiltonian matrix elements are uniquely determined by physical principles.

The method produces cutoff-independent physical quantities.

Application to phi-cubed theory illustrates the approach.

Abstract

We develop a systematic method for computing a renormalized light-front field theory Hamiltonian that can lead to bound states that rapidly converge in an expansion in free-particle Fock-space sectors. To accomplish this without dropping any Fock sectors from the theory, and to regulate the Hamiltonian, we suppress the matrix elements of the Hamiltonian between free-particle Fock-space states that differ in free mass by more than a cutoff. The cutoff violates a number of physical principles of the theory, and thus the Hamiltonian is not just the canonical Hamiltonian with masses and couplings redefined by renormalization. Instead, the Hamiltonian must be allowed to contain all operators that are consistent with the unviolated physical principles of the theory. We show that if we require the Hamiltonian to produce cutoff-independent physical quantities and we require it to respect the unviolated physical principles of the theory, then its matrix elements are uniquely determined in terms of the fundamental parameters of the theory. This method is designed to be applied to QCD, but for simplicity, we illustrate our method by computing and analyzing second- and third-order matrix elements of the Hamiltonian in massless phi-cubed theory in six dimensions.