We propose a new mechanism to produce a fermion mass hierarchy dynamically ina model with a singlet generation of fermions. A five dimensional gauge theoryon an interval with point interactions (zero-width branes) takes responsibilityfor realizing three generations and each massless zero mode localizes atboundaries of the segments on the extra dimension. An extra-dimensioncoordinate-dependent vacuum expectation value of a scalar field makes largedifferences in overlap integrals of the localized zero modes and then anexponential fermion mass hierarchy can appear. The positions of the pointinteractions control the magnitude of the fermion mass hierarchy and aredetermined by the minimization condition of the Casimir energy. As a result ofthe minimization of the Casimir energy, an exponential mass hierarchy appearsdynamically. We also discuss the stability of the extra dimension.
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