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

Abstract

The unified $(p,q;\alpha ,\gamma ,l)$-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 $U_{pq}^{\alpha \gamma l}(su(2))$ algebra by the generalized $(p,q;\alpha ,\gamma ,l)$-deformed operators are found. The generalized $(p,q;\alpha ,\gamma ,l)$-deformation of the two-dimensional conformal field theory is established. By introducing the $(p,q;\alpha ,\gamma ,l)$-operator product expansion (OPE) between the energy momentum tensor and primary fields, we obtain the $(p,q;\alpha ,\gamma ,l)$-deformed centerless Virasoro algebra. The two-point correlation function of the primary generalized $(p,q;\alpha ,\gamma ,l)$-deformed fields is calculated.

14 pages

References in corpus (4)

• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Representation Theory of Generalized Deformed Oscillator Algebras
• Conformal Properties of Primary Fields in a q-Deformed Theory
• Some comments on $q$-deformed oscillators and $q$-deformed $su(2)$ algebras

Cited by in corpus (2)

• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• The algebra of two dimensional generalized Chebyshev - Koornwinder oscillator