An algebra of deformation quantization for star-exponentials on complex symplectic manifolds

Abstract

The cotangent bundle $T^*X$ to a complex manifold $X$ is classically endowed with the sheaf of \cor-algebras \W[T^*X] of deformation quantization, where \cor\eqdot \W[\rmptt] is a subfield of \C[[\hbar,\opb{\hbar}]. Here, we construct a new sheaf of \cor-algebras \TW[T^*X] which contains \W[T^*X] as a subalgebra and an extra central parameter $t$. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If $P$ is any section of order zero of \W[T^*X], we show that \exp(t\opb{\hbar} P) is well defined in \TW[T^*X].Comment: Latex file, 24 page