Symmetrization of the Berezin Star Product and Multiple Star Product Method

TL;DR

This paper introduces a multiple star product method that expresses certain star products via path integrals, demonstrating associativity in the large N limit and deriving the Kontsevich star product's path integral form.

Contribution

It presents a novel multiple star product approach that unifies various star products and recovers known properties like associativity and path integral representations.

Findings

Associativity of skew-symmetrized Berezin star product in large N limit

Path integral form of Kontsevich star product derived

Method applicable to multiple examples

Abstract

We construct a multiple star product method and by using this method, show that integral forms of some star products can be written in terms of the path-integral. This method can be applied to some examples. Especially, the associativity of the skew-symmetrized Berezin star product proposed in \cite{SW}, is recovered in large $N$ limit of the multiple star product. We also derive the path integral form of the Kontsevich star product from the multiple Moyal star product. This paper includes some reviews about star products.