Dirac Sea for Bosons I -- Formulation of Negative Energy Sea for Bosons

TL;DR

This paper proposes a novel formulation for second quantization of bosonic theories by extending the Dirac sea concept, introducing negative energy states and a new vacuum structure for bosons.

Contribution

It generalizes the Dirac sea concept to bosons, defining a new vacuum with negative energy states and a sector division, which is a novel approach in quantum field theory.

Findings

Introduces a negative energy boson sea concept.

Defines a vacuum with negative boson numbers.

Proposes a model with separate positive and negative sectors.

Abstract

It is proposed to make formulation of second quantizing a bosonic theory by generalizing the method of filling the Dirac negative energy sea for fermions. We interpret that the correct vacuum for the bosonic theory is obtained by adding minus one boson to each single particle negative energy states while the positive energy states are empty. The boson states are divided into two sectors ; the usual positive sector with positive and zero numbers of bosons and the negative sector with negative numbers of bosons. Once it comes into the negative sector it cannot return to the usual positive sector by ordinary interaction due to a barrier. It is suggested to use as a playground model in which the filling of empty fermion Dirac sea and the removal of boson from the negative energy states are not yet performed. We put forward such a naive vacuum world in the present paper. The successive paper will concern a CPT-like Theorem in the naive vacuum world.