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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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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