SU(2) coherent states on an m-sheeted covering of the sphere

Abstract

SU(2) coherent states on an m-sheeted covering of the sphere are introduced, and properties like overcompleteness and resolution of the identity are studied. Operators J+(m), J−(m), Jz(m) that obey the SU(2) algebra but shift the ‖jn〉 states by m steps are considered, and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the standard SU(2) coherent states with respect to the usual angular momentum operators J+, J−, Jz. An extended SU(2) Bargmann representation on an m-sheeted sphere is introduced in which the transformations of an m-sheeted covering of the SU(2) group are implemented as extended Mobius conformal mappings. The formalism is applied in the study of Hamiltonians that contain the operators J+(m), J−(m), Jz(m) and describe processes where the state of a particle is shifted by m steps. The method is also used in the context of both the Holstein–Primakoff and Schwinger representation of SU(2).