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On reproducing kernels and quantization of states. (English) Zbl 0645.53044

From the paper: “Quantization of a mechanical system with phase space a Kähler manifold is studied. It is shown that the calculation of the Feynman path integral for such a system is equivalent to finding the reproducing kernel function. The proposed approach is applied to a scalar massive conformal particle interacting with an external field which is described by the deformation of a Hermitian line bundle structure.”
Reviewer: K.Oeljeklaus

MSC:

53B50 Applications of local differential geometry to the sciences
53B35 Local differential geometry of Hermitian and Kählerian structures
53D50 Geometric quantization
32L05 Holomorphic bundles and generalizations
32G07 Deformations of special (e.g., CR) structures
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