A Family of Circular Bargmann Transforms
arXiv:1105.4350
Abstract
When considering a charged particle evolving in the Poincaré disk under influence of a uniform magnetic field with a strength proportional to +1, we construct for all hyperbolic Landau level ε^γ_ m = 4m(-m), m 2 Z+ \[0, /2] a family of coherent states transforms labeled by (,m) and mapping isometrically square integrable functions on the unit circle with respect to the measure sin^γ-2m (θ/2) dθonto spaces of bound states of the particle. These transforms are called circular Bargmann transforms.
8 pages