Differential technique for the covariant orbital angular momentum operators

TL;DR

This paper introduces a differential technique to simplify the calculation of covariant orbital angular momentum operators, especially useful for reactions involving high-spin particles in hadron physics.

Contribution

It develops a differential method for direct calculation of convolutions of orbital angular momentum operators with multiple Lorentz indices, enhancing computational efficiency.

Findings

Simplifies calculations involving high-spin particles

Enables direct computation of convolutions of angular momentum operators

Generalizes orbital angular momentum operators for broader applications

Abstract

The orbital angular momentum operator expansion turns to be a powerful tool to construct the fully covariant partial wave amplitudes of hadron decay reactions and hadron photo- and electroproduction processes. In this paper we consider a useful development of the orbital angular momentum operator expansion method. We present the differential technique allowing the direct calculation of convolutions of two orbital angular momentum operators with an arbitrary number of open Lorentz indices. This differential technique greatly simplifies calculations when the reaction subject to the partial wave analysis involves high spin particles in the initial and/or final states. We also present a useful generalization of the orbital angular momentum operators.