Symmetrization of the Berezin star product and multiple star product method

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 [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.