# A heat kernel proof of the index theorem for deformation quantization

## TL;DR

This paper presents a heat kernel proof of the algebraic index theorem in deformation quantization on pseudo-Kahler manifolds, simplifying the formula by normalizing trace densities and characteristic classes.

## Contribution

It introduces a heat kernel approach to prove the index theorem for deformation quantization with separation of variables, removing extraneous constants.

## Key findings

- Provides a simplified proof of the index theorem using heat kernel methods.
- Normalizes trace densities and characteristic classes to eliminate extra constants.
- Applies to deformation quantization on pseudo-Kahler manifolds.

## Abstract

We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canonical trace density of a star product and of the characteristic classes involved in the index formula for which this formula contains no extra constant factors.