Quantum Geometrical Phases and Mesoscopic Persistent Current

We critically examine the concepts of quantum geometrical phases which have been widely applied to calculate mesoscopic persistent currents in the current literature. We point out that the method used in these calculations is essentially in conflict with the basic concepts of quantum geometrical phases. We give an example calculation of mesoscopic ring Aharonov-Anandan, Aharonov-Casher phases and persistent current to show some of the misconceptions involved in the current literature.