Star product for deformed oscillator algebra Aq(2,ν) *

Abstract

Abstract An analogue of the Moyal star product is presented for the deformed oscillator algebra. It contains several homotopy-like additional integration parameters in the multiplication kernel generalizing the differential Moyal star product formula exp[iϵ αβ ∂ α ∂ β ]. Using Pochhammer formula Pochhammer (1890 Math. Ann. 35 495–526), integration over these parameters is carried over a Riemann surface associated with the expression of the type z x (1 − z) y where x and y are arbitrary real numbers. Procedure for perturbative expansion in deformation parameter for the product is provided.