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

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

Risultato della ricerca: Article

11 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

Fingerprint

Complex Polynomials
Hermite Polynomials
Bosons
Quantization
Complex Variables
Operator
Irreducible Representation
Invertible
Argand diagram
Phase Space
Resolve
Generalization

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

Cita questo

D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization. / Bagarello, Fabio; Bagarello, Fabio; Gazeau, Jean Pierre; Ali, S. Twareque.

In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, Vol. 11, 2015.

Risultato della ricerca: Article

Bagarello, F, Bagarello, F, Gazeau, JP & Ali, ST 2015, 'D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization', SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, vol. 11.
Bagarello F, Bagarello F, Gazeau JP, Ali ST. D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. 2015;11.
Bagarello, Fabio ; Bagarello, Fabio ; Gazeau, Jean Pierre ; Ali, S. Twareque. / D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization. In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. 2015 ; Vol. 11.
@article{8be8a89abdbc4d7693ef43277f13e47a,
title = "D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization",
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.",
author = "Fabio Bagarello and Fabio Bagarello and Gazeau, {Jean Pierre} and Ali, {S. Twareque}",
year = "2015",
language = "English",
volume = "11",
journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",
issn = "1815-0659",
publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization

AU - Bagarello, Fabio

AU - Bagarello, Fabio

AU - Gazeau, Jean Pierre

AU - Ali, S. Twareque

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/147458

UR - http://dx.doi.org/10.3842/SIGMA.2015.078

M3 - Article

VL - 11

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

ER -

Accesso al documento