Contravariant symbol quantization on $S^2$

TL;DR

This paper introduces an algebra of contravariant symbols on the sphere $S^2$ and provides an algebraic proof of the Correspondence Principle within this framework.

Contribution

It defines a new algebraic structure of contravariant symbols on $S^2$ and proves the Correspondence Principle algebraically.

Findings

Established an algebra of contravariant symbols on $S^2$

Provided an algebraic proof of the Correspondence Principle

Enhanced understanding of quantization on the sphere

Abstract

We define an algebra of contravariant symbols on $S^2$ and give an algebraic proof of the Correspondence Principle for that algebra.