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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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Інститут математики НАН України
2015
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147152 |
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irk-123456789-1471522019-02-14T01:26:06Z D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization Ali, S.T. Bagarello, F. Gazeau, J.P. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147152 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Ali, S.T. Bagarello, F. Gazeau, J.P. |
| spellingShingle |
Ali, S.T. Bagarello, F. Gazeau, J.P. D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ali, S.T. Bagarello, F. Gazeau, J.P. |
| author_sort |
Ali, S.T. |
| title |
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT alist dpseudobosonscomplexhermitepolynomialsandintegralquantization AT bagarellof dpseudobosonscomplexhermitepolynomialsandintegralquantization AT gazeaujp dpseudobosonscomplexhermitepolynomialsandintegralquantization |
| first_indexed |
2023-05-20T17:26:43Z |
| last_indexed |
2023-05-20T17:26:43Z |
| _version_ |
1796153311084150784 |