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.
Ali, S., Bagarello, F., Gazeau, J. (2015). D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 11 [10.3842/SIGMA.2015.078].
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
BAGARELLO, Fabio;
2015-01-01
Abstract
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.File | Dimensione | Formato | |
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