Abstract
For a long time, about 60 years, the phase as an observable of the quantized light fields has remained a fundamental problem with considerable difficulties on quantum mechanics and also quantum optics. Recently, however, the hermitian phase operator and its eigenstates in a finite Hilbert space are found by Pegg and Barnett. In this paper, we provide a historical review and the background of the problem on the phase operator, explore the Pegg-Barnett formalism, and show the recent developements of this fields and its application to various light fields. Further problems on this formalism and other approaches are also discussed.
