Normalized Weyl-type ⋆\star-product on K\"ahler manifolds

We define a normalized Weyl-type $\star$-product on general K\"{a}hler manifolds. Expanding this product perturbatively we show that the cumbersome term, which appears in a Berezin-type product, does not appear at least in the first order of $\hbar$. This means a normalization factor, which is introduced by Reshetikhin and Takhtajan for a Berezin-type product, is unnecessary for our Weyl-type product at that order.Comment: to be published in Mod. Phys. Lett.

Toric topology

We survey some results on toric topology.Comment: English translation of the Japanese article which appeared in "Sugaku" vol. 62 (2010), 386-41