Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization*

作者：Chowdhury, S. Hasibul Hassan^*; Ali, S. Twareque; Englis, Miroslav

来源：Journal of Physics A-Mathematical and Theoretical, 2017, 50(19): 195203.

DOI：10.1088/1751-8121/aa66a6

• coherent states
• Berezin-Toeplitz quantization
• reproducing kernel
• noncommutative geometry

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 Gnc. 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.

• 出版日期2017-5-12
• 单位南开大学