Izu Vaisman
Super-Geometric Quantization
Preprint series: ESI preprints

MSC:

58F06 Geometric quantization (applications of representation theory), See also {22E45, 81S10}

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 K\"ahler
manifolds and to cotangent bundles of Riemannian manifolds.

Keywords: geometric quantization, linear superspace, supercommutator