arXiv subjects

I. M. Burban

Publications and source records attributed to I. M. Burban.

5 recordsLinked to original sources

arXiv2013

Unified $(p,q; α,γ, l)$-deformation of oscillator algebra and two-dimensional conformal field theory

The unified $ (p,q; α,γ, l)$-deformation of a number of well-known deformed oscillator algebras is introduced.The deformation is constructed by imputing new free parameters into the structure functions and by generalizing the defining relations of these algebras. The generalized Jordan-Schwinger and Holstein-Primakoff realizations of the $U_{pq}^{αγl}(su(2))$ algebra by the generalized $ (p,q; α,γ, l)$-deformed operators are found. The generalized $ (p,q; α,γ, l)$-deformation of the two-dimensional conformal field theory is established. By introducing the $ (p,q; α,γ, l)$-operator product expansion (OPE) between the energy momentum tensor and primary fields, we obtain the $ (p,q; α,γ, l)$-deformed centerless Virasoro algebra. The two-point correlation function of the primary generalized $ (p,q; α,γ, l)$-deformed fields is calculated.

math-ph↗

arXiv2011

Generalized deformed oscillators in framework of unified (q;α,β,γ;ν)-deformation and their oscillator algebras

The aim of this paper is to review our results on description of the multi-parameter deformed oscillators and their oscillator algebras. We define generalized (q;α,β,γ;ν)-deformed oscillator algebra and study its irreducible representations. The Arik-Coon oscillator with the main relation aa^+ - q a^+a = 1, where q > 1 is embedded in this framework. We find connection of this oscillator with the Askey (1/q)-Hermite polynomials. We construct family of the generalized coherent states associated with these polynomials and give their explicit expression in terms of standard special functions. By means of the solution of appropriate classical Stielties moment problem we prove the (over)completeness relation of these states.

math-ph↗

arXiv2008

Unified $(q;α,β,γ;ν)$-deformation of one-parametric q-deformed oscillator algebras

We define a generalized $(q;α,β,γ;ν)$-deformed oscillator algebra and study the number of its characteristics. We describe the structure function of deformation, analyze the classification of irreducible representations and discuss the asymptotic spectrum behaviour of the Hamiltonian. For a special choice of the deformation parameters we construct the deformed oscillator with discrete spectrum of its "quantized coordinate" operator. We establish its connection with the (generalized) discrete Hermite I polynomials.

math-ph↗

arXiv2006

On (p, q; α, β, l)-deformed oscillators and their oscillator algebras

We present a description of a new kind of the deformed canonical commutation relations, their representations and generated by them Heisenberg-Weyl algebra. This deformed algebra allows us to derive operations of the Hopf algebra structure: comultiplication, counit and antipode. We discuss properties of a discrete spectrum of the Hamiltonian of the deformed harmonic oscillator corresponding to this oscillator-like system.

math.QA↗

arXiv2006

Generalized q-deformed oscillators, q-Hermite polynomials, generalized coherent states

The aim of this paper is to study generalized q-analogs of the well-known q-deformed harmonic oscillators and to connect them with q-Hermite polynomials. We give a construction of the appropriate oscillator-like algebras and show that corresponding Hermite polynomials are generalization of the discrete q-Hermite I and the discrete q-Hermite II polynomials. We also construct generalized coherent states of Barut-Girardello type for oscillator-like systems connected with these polynomials.

math-ph↗