Covariant phase difference observables in quantum mechanics

Covariant phase difference observables are determined in two different ways, by a direct computation and by a group theoretical method. A characterization of phase difference observables which can be expressed as the difference of two phase observables is given. The classical limits of such phase difference observables are determined and the Pegg-Barnett phase difference distribution is obtained from the phase difference representation. The relation of Ban’s theory to the covariant phase theories is exhibited.