Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane

P. Hurtado, A. Leones and J. B. Moreno

Abstract and Applied Analysis, 2020, vol. 2020, 1-7

Abstract:

Using standard techniques from geometric quantization, we rederive the integral product of functions on (non-Euclidian) which was introduced by Pierre Bieliavsky as a contribution to the area of strict quantization. More specifically, by pairing the nontransverse real polarization on the pair groupoid , we obtain the well-defined integral transform. Together with a convolution of functions, which is a natural deformation of the usual convolution of functions on the pair groupoid, this readily defines the Bieliavsky product on a subset of .

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:6794709

DOI: 10.1155/2020/6794709

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