Deformation Quantization for Supermanifolds via Gelfand-Kazhdan Descent

TL;DR

This paper develops a canonical deformation quantization method for symplectic supermanifolds, providing a new proof of the super-analogue of Fedosov quantization using Gelfand-Kazhdan descent formalism.

Contribution

It introduces a novel approach to supermanifold quantization by applying Gelfand-Kazhdan descent, extending Fedosov's method to the super-symplectic context.

Findings

Constructed a canonical deformation quantization for symplectic supermanifolds.

Provided a new proof of the super-analogue of Fedosov quantization.

Established foundations for Gelfand-Kazhdan descent in the super-symplectic setting.

Abstract

We construct a canonical deformation quantization for symplectic supermanifolds. This gives a novel proof of the super-analogue of Fedosov quantization. Our proof uses the formalism of Gelfand-Kazhdan descent, whose foundations we establish in the super-symplectic setting.