  The Pauli-Villars regularization is appropriate to discuss the UV sensitivity
of low-energy observables because it mimics how the contributions of new
particles at high energies cancel large quantum corrections from the light
particles in the effective field theory. We discuss the UV sensitivity of the
Casimir energy density and pressure in an extra-dimensional model in this
regularization scheme, and clarify the condition on the regulator fields to
preserve the Lorentz symmetry of the vacuum state. Some of the conditions are
automatically satisfied in spontaneously-broken supersymmetric models, but
supersymmetry is not enough to ensure the Lorentz symmetry. We show that the
necessary regulators can be introduced as bulk fields. We also evaluate the
Casimir energy density with such regulators, and its deviation from the result
obtained in the analytic regularization.
