Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane
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 gro...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2020/6794709 |
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| author | P. Hurtado A. Leones J. B. Moreno |
| author_facet | P. Hurtado A. Leones J. B. Moreno |
| author_sort | P. Hurtado |
| collection | DOAJ |
| description | 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 L2ℝ2. |
| format | Article |
| id | doaj-art-ebc86909be3047ef9c3e40e5b3332960 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ebc86909be3047ef9c3e40e5b33329602025-02-03T01:28:22ZengWileyAbstract and Applied Analysis1085-33751687-04092020-01-01202010.1155/2020/67947096794709Strict Deformation Quantization via Geometric Quantization in the Bieliavsky PlaneP. Hurtado0A. Leones1J. B. Moreno2Facultad de Ciencias Básicas e Ingenieria, Uniremington, Medellín Antioquia, ColombiaFacultad de Ciencias Básicas e Ingenieria, Uniremington, Medellín Antioquia, ColombiaFacultad de Ciencias Básicas e Ingenieria, Uniremington, Medellín Antioquia, ColombiaUsing 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 L2ℝ2.http://dx.doi.org/10.1155/2020/6794709 |
| spellingShingle | P. Hurtado A. Leones J. B. Moreno Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane Abstract and Applied Analysis |
| title | Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane |
| title_full | Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane |
| title_fullStr | Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane |
| title_full_unstemmed | Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane |
| title_short | Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane |
| title_sort | strict deformation quantization via geometric quantization in the bieliavsky plane |
| url | http://dx.doi.org/10.1155/2020/6794709 |
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