D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization

Fabio Bagarello, Fabio Bagarello, Jean Pierre Gazeau, S. Twareque Ali

Risultato della ricerca: Articlepeer review

13 Citazioni (Scopus)

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.
Lingua originaleEnglish
Numero di pagine23
RivistaSYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
Volume11
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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