Gauge Invariant Regularization of Quantum Field Theory on the Light-Front

TL;DR

This paper presents a gauge invariant regularization method for quantum field theory on the Light-Front, using a transverse lattice and boundary conditions, simplifying constraints and aiding low-energy model formulation.

Contribution

It introduces a novel gauge invariant regularization scheme on the Light-Front that simplifies the canonical formalism and constraints, applicable to both standard and effective gauge theories.

Findings

Regularization removes ultraviolet divergences in longitudinal momentum

The formalism simplifies the constraints by eliminating second class constraints

Discusses challenges in defining the vacuum due to Lorentz invariance issues

Abstract

Gauge invariant regularization of quantum field theory in the framework of Light-Front (LF) Hamiltonian formalism via introducing a lattice in transverse coordinates and imposing boundary conditions in LF coordinate $x^-$ for gauge fields on the interval $|x^-|\le L$ is considered. The remaining ultraviolet divergences in the longitudinal momentum $p_-$ are removed by gauge invariant finite mode regularization. We find that LF canonical formalism for the introduced regularization does not contain usual most complicated second class constraints connecting zero and nonzero modes of gauge fields. The described scheme can be used either for the regularization of conventional gauge theory or for gauge invariant formulation of effective low-energy models on the LF. The lack of explicit Lorentz invariance in our approach leads to difficulty with defining the vacuum state. We discuss this difficulty, particulary, in the connection with the problem of taking the limit of continuous space.