Comparison of quantum field perturbation theory for the light front with the theory in lorentz coordinates

TL;DR

This paper investigates the differences between light-front and Lorentz-covariant perturbation theories, proposing a method to construct counter-terms to reconcile the two, with explicit results for the Yukawa model.

Contribution

It introduces a novel method to identify and compensate differences between light-front and Lorentz perturbation series without explicit calculations.

Findings

Derived a closed-form light-front Hamiltonian with counter-terms for the Yukawa model.

Proposed a general procedure for constructing counter-terms at any finite order.

Discussed potential applications to gauge theories.

Abstract

The relationship between the perturbation theory in light-front coordinates and Lorentz-covariant perturbation theory is investigated. A method for finding the difference between separate terms of the corresponding series without their explicit evaluation is proposed. A procedure of constructing additional counter-terms to the canonical Hamiltonian that compensate this difference at any finite order is proposed. For the Yukawa model, the light-front Hamiltonian with all of these counter-terms is obtained in a closed form. Possible application of this approach to gauge theories is discussed.