Dirac Sea and Hole Theory for Bosons II -- Renormalization Approach --

TL;DR

This paper introduces a renormalization approach to construct a positive definite inner product in the negative energy bosonic Dirac sea, clarifying the analytical properties of the formulation.

Contribution

It proposes an $psilon$-regularization and renormalization method to improve the mathematical understanding of the bosonic Dirac sea.

Findings

Successful construction of a positive definite inner product

Enhanced analytical clarity of the bosonic Dirac sea formulation

Potential applications to quantum field theory

Abstract

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.