Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds

The purpose of this paper is to construct non-perturbative deformation quantizations of the algebras of smooth functions on Poisson supermanifolds. For the examplesU ^1¦1 andC ^m¦n , algebras of super Toeplitz operators are defined with respect to certain Hilbert spaces of superholomorphic functions. Generators and relations for these algebras are given. The algebras can be thought of as algebras of quantized functions, and deformation conditions are proven which demonstrate the recovery of the super Poisson structures in a semi-classical limit.Supported in part by the Department of Energy under grant DE-FG02-88ER25065Supported in part by the Italian National Institute for Nuclear Physics (INFN)