D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
- Autori: Ali, S.; Bagarello, F.; Gazeau, J.
- Anno di pubblicazione: 2015
- Tipologia: Articolo in rivista (Articolo in rivista)
- OA Link: http://hdl.handle.net/10447/147458
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.