  In bosonic formulation of the negative energy sea, so called Dirac sea
presented in the preceding paper [arXiv:hep-th/0603242], one of the crucial
points is how to construct a positive definite inner product in the negative
energy states, since naive attempts would lead to non-positive definite ones.
In the preceding paper the non-local method is used to define the positive
definite inner product. In the present article we make use of a kind of
$\epsilon$-regularization and renormalization method which may clarify
transparently the analytical properties of our formulation.
