Symmetrization of Berezin Star Product and Path-Integral Quantization

TL;DR

This paper introduces a new star product interpolating Berezin and Moyal quantization, linking it to path-integral quantization and string theory, and discusses its relation to Kontsevich's approach.

Contribution

It proposes a novel star product bridging Berezin and Moyal quantizations and connects it to path-integral and string theory frameworks.

Findings

The new star product reduces to path-integral quantization in the continuous limit.

In flat space, the action corresponds to free bosonic strings.

Relation to Kontsevich's quantization prescription is established.

Abstract

We propose a new star pruduct which interpolates the Berezin and Moyal quantization. A multiple of this product is shown to reduce to a path-integral quantization in the continuous time limit. In flat space the action becomes the one of free bosonic strings. Relation to Kontsevich prescription is also discussed.