### Abstract

Original language | English |
---|---|

Number of pages | 23 |

Journal | SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS |

Volume | 11 |

Publication status | Published - 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

*SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS*,

*11*.

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

Research output: Contribution to journal › Article

*SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS*, vol. 11.

}

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 -