Renormalization of Hamiltonians in the Light-Front Fock Space

TL;DR

This paper presents a method for ultraviolet renormalization of Hamiltonians in light-front Fock space, maintaining symmetries and demonstrating calculations in Yukawa theory, QED, and QCD.

Contribution

It introduces a renormalization procedure for light-front Hamiltonians that preserves kinematical symmetries and applies it to key quantum field theories.

Findings

Successful second order calculations of self-energy and interaction terms.

Preservation of light-front symmetries during renormalization.

Infrared singularities are regulated but not renormalized.

Abstract

We outline an ultraviolet renormalization procedure for hamiltonians acting in the light-front Fock space. The hamiltonians are defined and calculated using creation and annihilation operators with no limitation of the space of states. Both, the regularization of the initial hamiltonian and the definition of the renormalized effective hamiltonians, preserve the light-front frame kinematical symmetries. The general equations for the effective hamiltonians are illustrated by second order calculations of the self-energy and two-particle interaction terms in Yukawa theory, QED and QCD. Infrared singularities are regulated but not renormalized.