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Current issue   Ukr. J. Phys. 2014, Vol. 58, N 11, p.1113-1120
doi:10.15407/ujpe58.11.1113    Paper

Burban I.M.

Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrologichna Str., Kyiv 03680, Ukraine; e-mail: burban@bitp.kiev.ua)

Unified (p, q; α, γ, l)-Deformations of Oscillator and Hybrid Oscillator Algebras and Two-Dimensional Conformal Field Theory

Section: International Conference “Quantum Groups and Quantum Integrable Systems” Kyiv, June 18–21, 2013
Original Author's Text: English

Abstract: The unified multiparametric generalizations of the well-known two-parameter deformed oscillator and hybrid oscillator algebras are introduced. The basic versions of these deformations are obtained by imputing the new free parameters in the structure functions and by a generalization of defining relations of these algebras. The generalized Jordan–Schwinger and Holstein– Primakoff realizations of the Ulpq (su(2)) algebra by the creations and annihilations operators of the basic versions of these deformations are found. The (p, q; α, γ, l)-deformation of the two-dimensional conformal field theory is considered. The pole structure of the (p, q; α, γ, l)- deformed operator product expansion (OPE) of the holomorphic component of the energymomentum tensor with primary fields is found. The two-point correlation function of the (p, q; α, γ, l)-deformed two-dimensional conformal field theory is calculated.

Key words: generalized deformed oscillator algebra, structure function, generalized Jordan– Schwinger and Holstein–Primakoff transformations, deformed two-dimensional conformal field theory.