Cayley transforms of su(2) representations

TL;DR

This paper presents explicit Cayley transform formulas for su(2) representations as spin matrix polynomials and compares them to existing exponential matrix polynomial forms.

Contribution

It introduces explicit Cayley transform polynomials for su(2) spins and compares them with known exponential forms, providing new computational tools.

Findings

Cayley transforms are expressed as explicit spin matrix polynomials.

Comparison shows differences and similarities with exponential matrix polynomials.

Provides formulas applicable to any spin j representation.

Abstract

Cayley rational forms for rotations are given as explicit spin matrix polynomials for any j. The results are compared to the Curtright-Fairlie-Zachos matrix polynomials for rotations represented as exponentials.