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The phase shift due to the Sagnac Effect, for relativistic matter beamscounter-propagating in a rotating interferometer, is deduced on the bases of aa formal analogy with the the Aharonov-Bohm effect. A procedure outlined bySakurai, in which non relativistic quantum mechanics and newtonian physicsappear together with some intrinsically relativistic elements, is generalizedto a fully relativistic context, using the Cattaneo's splitting technique. Thisapproach leads to an exact derivation, in a self-consistently relativistic way,of the Sagnac effect. Sakurai's result is recovered in the first orderapproximation.Comment: 18 pages, LaTeX, 2 EPS figures. To appear in General Relativity and  Gravitatio

The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams