Noncommutative coherent states and related aspects of Berezin–Toeplitz quantization

In this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of $G_{nc}$, a connected, simply connected nilpotent Lie group, which was identified as the kinematical symmetry group of noncommutative quantum mechanics for a system of two degrees of freedom in an earlier paper. Similarly described are the degenerate noncommutative coherent states arising from the degenerate UIRs of $G_{nc}$. We then compute the reproducing kernels associated with both these families of coherent states and study the Berezin–Toeplitz quantization of the observables on the underlying 4-dimensional phase space, analyzing in particular the semi-classical asymptotics for both these cases. (paper)