  We show that the observed quark/lepton mass hierarchy can be realized
dynamically on an interval extra dimension with point interactions. In our
model, the positions of the point interactions play a crucial role to control
the quark/lepton mass hierarchy and are determined by the minimization of the
Casimir energy. By use of the exact extra-dimensional coordinate-dependent
vacuum expectation value of a gauge singlet scalar, we find that there is a
parameter set, where the positions of the point interactions are stabilized and
fixed, which can reproduce the experimental values of the quark masses
precisely enough, while the charged lepton part is less relevant. We also show
that possible mixings among the charged leptons will improve the situation
significantly.
