Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization

Abstract

In~this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of $\g$, a connected, simply connected nilpotent Lie group, that was identified as the kinematical symmetry group of noncommutative quantum mechanics for a system of 2-degrees of freedom in an earlier paper. Likewise described are the degenerate noncommutative coherent states arising from the degenerate UIRs of $\g$. We~then compute the reproducing kernels associated with both these families of coherent states and study Berezin-Toeplitz quantization of the observables on the underlying 4-dimensional phase space, analyzing in particular the semi-classical asymptotics for both these cases.

22 pages, no figure

References in corpus (4)

• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Magnetic fields in noncommutative quantum mechanics
• Wigner Functions for Noncommutative Quantum Mechanics: a group representation based construction
• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori

Cited by in corpus (1)

• New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis