Deformation quantization with separation of variables on a super-K\"ahler manifold

TL;DR

This paper develops a method for deformation quantization on super-K"ahler manifolds, focusing on separation of variables, and describes their canonical supertrace densities, advancing mathematical tools in supergeometry.

Contribution

It introduces deformation quantizations with separation of variables on split super-K"ahler manifolds and characterizes their canonical supertrace densities, a novel extension in supergeometry.

Findings

Constructed deformation quantizations with separation of variables.

Described canonical supertrace densities for these quantizations.

Extended deformation quantization techniques to super-K"ahler manifolds.

Abstract

We construct deformation quantizations with separation of variables on a split super-K\"ahler manifold and describe their canonical supertrace densities.