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, issue 1

Abstract: Using standard techniques from geometric quantization, we rederive the integral product of functions on ℝ2 (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 ℝ2×ℝ¯2, 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 L2(ℝ2).

Date: 2020
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https://doi.org/10.1155/2020/6794709

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2020:y:2020:i:1:n:6794709

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