Sagnac effect as viewed by a co-rotating observer

The authors consider the Sagnac effect from the point of view of a co-rotating observer. They give for both matter and light waves the fully relativistic evolution equations in the rotating frame of reference. In the nonrelativistic limit the Sagnac effect is similar to the Aharonov-Bohm effect. This similarity shows that the Sagnac effect is a manifestation of Berry's phase.