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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2015, том 11, 078, 23 стр. (Mi sigma1059)

Эта публикация цитируется в 13 статьях

$\mathcal{D}$-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization

S. Twareque Alia, Fabio Bagarellobc, Jean Pierre Gazeaude

a Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada H3G 1M8
b INFN, Torino, Italy
c Dipartimento di Energia, ingegneria dell’Informazione e modelli Matematici, Scuola Politecnica, Università di Palermo, I-90128 Palermo
d Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, 22290-180 Rio de Janeiro, Brazil
e APC, UMR 7164, Univ Paris Diderot, Sorbonne Paris-Cité, 75205 Paris, France

Аннотация: The $\mathcal{D}$-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 $\mathrm{GL}(2,\mathbb{C})$ of invertible $2 \times 2$ 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.

Ключевые слова: pseudo-bosons; coherent states; quantization; complex Hermite polynomials; finite group representation.

MSC: 81Q12; 47C05; 81S05; 81R30; 33C45

Поступила: 28 марта 2015 г.; в окончательном варианте 21 сентября 2015 г.; опубликована 1 октября 2015 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2015.078



Реферативные базы данных:
ArXiv: 1509.03822


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