D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
The D-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group GL(2,C) of invertible 2×2 matrices with complex entries. It reveals interesting aspects of these represen...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147152 |
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| Cite this: | D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization / S.T. Ali, F. Bagarello, J.P. Gazeau // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 41 назв. — англ. |
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Ali, S.T. Bagarello, F. Gazeau, J.P. 2019-02-13T17:44:41Z 2019-02-13T17:44:41Z 2015 D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization / S.T. Ali, F. Bagarello, J.P. Gazeau // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q12; 47C05; 81S05; 81R30; 33C45 DOI:10.3842/SIGMA.2015.078 https://nasplib.isofts.kiev.ua/handle/123456789/147152 The D-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group GL(2,C) of invertible 2×2 matrices with complex entries. It reveals interesting aspects of these representations. The second example is based on a pseudo-bosonic generalization of operator-valued functions of a complex variable which resolves the identity. We show that such a generalization allows one to obtain a quantum pseudo-bosonic version of the complex plane viewed as the canonical phase space and to understand functions of the pseudo-bosonic operators as the quantized versions of functions of a complex variable. The authors are indebted to referees for their relevant and constructive comments and suggestions. They acknowledge financial support from the Universit`a di Palermo. S.T.A. acknowledges a grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada, F.B. acknowledges support from GNFM, J.P.G. thanks the CBPF and the CNPq for financial support and CBPF for hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization |
| spellingShingle |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization Ali, S.T. Bagarello, F. Gazeau, J.P. |
| title_short |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization |
| title_full |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization |
| title_fullStr |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization |
| title_full_unstemmed |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization |
| title_sort |
d-pseudo-bosons, complex hermite polynomials, and integral quantization |
| author |
Ali, S.T. Bagarello, F. Gazeau, J.P. |
| author_facet |
Ali, S.T. Bagarello, F. Gazeau, J.P. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The D-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group GL(2,C) of invertible 2×2 matrices with complex entries. It reveals interesting aspects of these representations. The second example is based on a pseudo-bosonic generalization of operator-valued functions of a complex variable which resolves the identity. We show that such a generalization allows one to obtain a quantum pseudo-bosonic version of the complex plane viewed as the canonical phase space and to understand functions of the pseudo-bosonic operators as the quantized versions of functions of a complex variable.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147152 |
| citation_txt |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization / S.T. Ali, F. Bagarello, J.P. Gazeau // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 41 назв. — англ. |
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2025-12-07T19:47:17Z |
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2025-12-07T19:47:17Z |
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