Feynman perturbation theory for gauge theory on transverse lattice

TL;DR

This paper develops a Feynman perturbation theory for nonabelian gauge theories on a transverse lattice, aiming to preserve gauge invariance and rotational symmetry while analyzing divergence-free diagrams and discussing renormalization.

Contribution

It introduces a novel lattice-based approach for gauge theories using non-unitary matrices to maintain polynomial action and symmetry properties, advancing regularization techniques.

Findings

Identified divergence-free diagrams in the lattice gauge theory

Proposed a renormalization scheme compatible with lattice regularization

Maintained rotational invariance in the discretized gauge theory

Abstract

Feynman perturbation theory for nonabelian gauge theory in light-like gauge is investigated. A lattice along two space-like directions is used as a gauge invariant ultraviolet regularization. For preservation of the polinomiality of action we use as independent variables arbitrary (non-unitary) matrices related to the link of the lattice. The action of the theory is selected in such a way to preserve as much as possible the rotational invariance, which remains after introduction of the lattice, as well as to make superfluous degrees of freedom vanish in the limit of removing the regularization. Feynman perturbation theory is constructed and diagrams which does not contain ultraviolet divergences are analyzed. The scheme of renormalization of this theory is discussed.