Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem

TL;DR

This paper introduces a novel field quantization method using an indefinite metric and negative energy fields to cancel vacuum energy, addressing the cosmological constant problem through charge conjugation symmetry and a Dirac sea approach.

Contribution

It proposes a new quantization framework with negative energy fields and para-statistics to stabilize the vacuum and cancel the cosmological constant.

Findings

Zero-point vacuum energy cancels due to charge conjugation symmetry.

Vacuum stability achieved via a Dirac sea of negative energy particles.

Negative energy bosons obey para-statistics, preventing their observability.

Abstract

We propose a method of field quantization which uses an indefinite metric in a Hilbert space of state vectors. The action for gravity and the standard model includes, as well as the positive energy fermion and boson fields, negative energy fields. The Hamiltonian for the action leads through charge conjugation invariance symmetry of the vacuum to a cancellation of the zero-point vacuum energy and a vanishing cosmological constant in the presence of a gravitational field. To guarantee the stability of the vacuum, we introduce a Dirac sea `hole' theory of quantization for gravity as well as the standard model. The vacuum is defined to be fully occupied by negative energy particles with a hole in the Dirac sea, corresponding to an anti-particle. We postulate that the negative energy bosons in the vacuum satisfy a para-statistics that leads to a para-Pauli exclusion principle for the negative energy bosons in the vacuum, while the positive energy bosons in the Hilbert space obey the usual Bose-Einstein statistics. This assures that the vacuum is stable for both fermions and bosons. Restrictions on the para-operator Hamiltonian density lead to selection rules that prohibit positive energy para-bosons from being observable. The problem of deriving a positive energy spectrum and a consistent unitary field theory from a pseudo-Hermitian Hamiltonian is investigated.