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The Kaluza-Klein theory and Randall-Sundrum theory are examinedcomparatively, with focus on the behavior of the five dimensional (Dirac)fermion in the dimensional reduction to four dimensions. They are properlytreated using the Cartan formalism. In the KK case, the dual property betweenthe electric and magnetic dipole moments is revealed in relation to the ratioof two massive parameters: the inverse of the radius of the extra-space circleand the 5D fermion mass. The order estimation of the couplings is done. In theRS case, we consider the interaction with the 5D(bulk) Higgs field and thegauge field. The chiral property, localization, anomaly phenomena are examined.We evaluate the bulk quantum effect using the method of the induced effectiveaction. The electric dipole moment term naturally appears. This is a new originof the CP-violation. In the 4D limit, the dual relation between KK model and RSmodel appears.Comment: 30 pages, 4 figures, Typographical errors are correcte

Fermions in Kaluza-Klein and Randall-Sundrum theories