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

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 U αγl pq (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. K e y w o r d s: generalized deformed oscillator algebra, structure function, generalized Jordan-Schwinger and Holstein-Primakoff transformations, deformed two-dimensional conformal field theory.