An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces

Abstract EN

Consider the space L2(ℂ,dμ(z)), where dμ(z)=e−|z|2dz∧dz¯ is the Gaussian measure, and its generalized Bargmann subspaces Em which are the null kernels of the operator Δ=-∂2/∂z∂z¯+z¯(∂/∂z¯)-mI; m=0,1,….

In this work, we present an other construction of Em following the Hermite functions which allows us to define a family of generalized Bargmann transform Bm which maps isometrically Em into L2(ℝ).

The generalized coherent states ∣z〉m associated to Em are constructed and some properties of them are given.