Symmetrization of the Berezin star product and multiple star product method

We construct a multiple star product method and, using this method, show that integral forms of some star products can be written in terms of the path integral. The method is applied to some examples. In particular, the associativity of the skew-symmetrized Berezin star product proposed by Saito and Wakatsuki is recovered in the 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 a review of star products. (author)