ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 64,   1   (1995)
pp.   99-111
SUPER-GEOMETRIC QUANTIZATION
I. VAISMAN

Abstract.  Let $K$ be the complex line bundle where the Kostant-Souriau geometric quantization operators are defined. We discuss possible prolongations of these operators to the linear superspace of the $K$-valued differential forms, such that the Poisson bracket is represented by the supercommutator of the corresponding operators. We also discuss the possibility to obtain such super-geometric quantizations by (anti)Hermitian operators on a Hilbert superspace. We apply our general considerations to Kahler manifolds and to cotangent bundles of Riemannian manifolds.

AMS subject classification.  58F06
Keywords.  Geometric quantization, linear superspace, supercommutator
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