Invariant star-products on S^2 and the canonical trace

TL;DR

This paper proves the equivalence of two descriptions of invariant star-products on the 2-sphere, computes the canonical trace, and determines the characteristic class using the Fedosov-Nest-Tsygan index theorem.

Contribution

It establishes the equivalence of two existing descriptions of invariant star-products on S^2 and computes their characteristic class via index theory.

Findings

The two descriptions of invariant star-products on S^2 are shown to be the same.

The canonical trace of the star-product is explicitly calculated.

The characteristic class of the star-product is determined using the Fedosov-Nest-Tsygan index theorem.

Abstract

In the literature there are two different ways of describing an invariant star product on $S^2$. We show that the products are actually the same. We also calculate the canonical trace and use the Fedosov-Nest-Tsygan index theorem to obtain the characteristic class of this product.