SU(2) and SU(1,1) phase states

Phase operators and phase states are introduced in the Hilbert space H₂ⱼ₊₁ associated with the SU(2) group. The phase operators obey the SU(2) algebra and play a dual role to the standard angular-momentum operators. A finite Weyl group plays a fundamental role in those ideas. In the SU(1,1) case the exponential of the phase operators is nonunitary, and the phase states form an overcomplete set which is used to formulate an analytic representation.