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On reproducing kernels and quantization of states

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Abstract

Quantization of a mechanical system with the 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 deformation of a Hermitian line bundle structure.

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Authors and Affiliations

  1. Institute of Physics, Warsaw University Division in Białystok, 15-424 Białystok, PL-41, Lipowa, Poland

    Anatol Odzijewicz

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  1. Anatol Odzijewicz
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Communicated by R. Haag

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Odzijewicz, A. On reproducing kernels and quantization of states. Commun.Math. Phys. 114, 577–597 (1988). https://doi.org/10.1007/BF01229456

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  • DOI: https://doi.org/10.1007/BF01229456

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