Monogenic functions and representations of nilpotent Lie groups in quantum mechanics

We describe several different representations of nilpotent step two Lie groups in spaces of monogenic Clifford‐valued functions. We are inspired by the classic representation of the Heisenberg group in the Segal–Bargmann space of holomorphic functions. Connections with quantum mechanics are described. Copyright © 1999 John Wiley & Sons, Ltd.     

Characterization of Multidimensional Euclidean Landau States by Coherent State Transformations

We deal with a family of multidimensional generalized coherent states obtained using the Fock–Bargmann representation of the Heisenberg group. We prove that the ranges of the corresponding coherent state transformations coincide with the spaces of bound states of an even-dimensional analogue of a charged particle in a uniform magnetic field. This provides a new characterization of Euclidean Landau states.