Renormalization of gauge invariant composite operators in light-cone gauge

TL;DR

This paper extends renormalization techniques for composite operators in light-cone gauge, showing gauge-invariant operators form closed classes under renormalization with finite elements, simplifying their mixing behavior.

Contribution

It introduces a generalized framework for renormalizing gauge-invariant composite operators in light-cone gauge, highlighting their closed classes and simplified mixing structure.

Findings

Gauge-invariant operators form closed classes under renormalization.

Operators only mix within their classes, simplifying analysis.

Effective hierarchy ensures finite elements per class.

Abstract

We generalize to composite operators concepts and techniques which have been successful in proving renormalization of the effective Action in light-cone gauge. Gauge invariant operators can be grouped into classes, closed under renormalization, which is matrix-wise. In spite of the presence of non-local counterterms, an ``effective" dimensional hierarchy still guarantees that any class is endowed with a finite number of elements. The main result we find is that gauge invariant operators under renormalization mix only among themselves, thanks to the very simple structure of Lee-Ward identities in this gauge, contrary to their behaviour in covariant gauges.