Covariant phase difference observables

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 difference of two phase observables is given. Classical limit 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.