Harmonic Analysis and Applications

June 4-8, 2018


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

Englis, Miroslav

We construct `noncommutative' coherent states using families of unitary irreducible representations of a connected simply connected nilpotent Lie group, that represents the kinematical symmetry group of noncommutative quantum mechanics for a system of 2 degrees of freedom. The associated reproducing kernels lead to a `noncommutative' Berezin-Toeplitz quantization of the observables on the underlying 4-dimensional phase space, and we analyze in particular the arising semi-classical asymptotics. The topic makes contact both with mathematical physics and geometry, on the one hand, as well as with harmonic and complex analysis, on the other hand.

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