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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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