Reduction formulas for symmetric products of spin matrices

TL;DR

This paper derives identities for symmetric products of SU(2) spin matrices of any dimension, simplifying their expressions and highlighting their relevance in describing electromagnetic interactions of particles.

Contribution

It introduces reduction formulas for symmetric products of SU(2) generators of arbitrary dimension, providing a new mathematical tool for particle interaction analysis.

Findings

Derived identities for symmetric products of SU(2) matrices

Expressed symmetric products of D matrices in terms of fewer matrices

Highlighted importance in electromagnetic interaction characterization

Abstract

We show that, for SU(2) generators of arbitrary dimension $D$, there exist identities that express the completely symmetric product of $D$ matrices in terms of completely symmetric products of fewer number of matrices. We also indicate why such identities are important in characterizing electromagnetic interactions of particles.