Berezin-Toeplitz operators, a semi-classical approach

Abstract: This article is devoted to the Toeplitz Operators [4] in the context of the geometric quantization [11], [15]. We propose an ansatz for their Schwartz kernel. From this, we deduce the main known properties of the principal sym-bol of these operators and obtain new results: we dene their covariant and contravariant symbols, which are full symbol, and compute the product of these symbols in terms of the Kahler metric. This gives canonical star products on the Kahlerian manifolds. This ansatz is also useful to introduce the notion of microsupport