2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/206556In 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 $ε$-regularization and renormalization method which may clarify transparently the analytical properties of our formulation.10 pages, 2 figures; Section 4 is insertedHigh Energy Physics - Theorytext