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D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
Інший ID:
2010 Mathematics Subject Classification: 81Q12; 47C05; 81S05; 81R30; 33C45
DOI:10.3842/SIGMA.2015.078
DOI:10.3842/SIGMA.2015.078
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
469
Завантажень:
230
Анотація:
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.
