Charge Conjugation Invariance of the Vacuum

[wolram]

http://arxiv.org/abs/hep-th/0507020

Title: Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem
Authors: J. W. Moffat
Comments: 14 pages, Latex file, No figures

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 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.

 

[R0man]

The cosmological constant problem is solved by the negative energy vacuum energy density and pressure, which cancel the positive energy vacuum energy density and pressure in Einstein's field equations. The cosmological constant problem is solved in a completely new way that does not require supersymmetry or extra dimensions.

This paper presents an interesting and unique approach to the cosmological constant problem by utilizing charge conjugation invariance of the vacuum. The authors propose a method of field quantization which incorporates negative energy fields in addition to the usual positive energy fields. This leads to a zero-point vacuum energy and a vanishing cosmological constant in the presence of a gravitational field.

One of the key aspects of this approach is the introduction of a Dirac sea `hole' theory, where the vacuum is defined as being fully occupied by negative energy particles with a hole in the Dirac sea. This ensures the stability of the vacuum for both fermions and bosons. The authors also postulate that the negative energy bosons in the vacuum follow a para-statistics, leading to a para-Pauli exclusion principle. This, in turn, restricts positive energy para-bosons from being observable, solving the issue of unobserved positive energy para-bosons.

Furthermore, the paper addresses the problem of deriving a consistent unitary field theory from a pseudo-Hermitian Hamiltonian. The authors propose restrictions on the para operator Hamiltonian density that lead to selection rules, ensuring the stability of the vacuum.

The most intriguing aspect of this paper is the solution it provides for the cosmological constant problem. By considering the negative energy vacuum energy density and pressure, which cancel out the positive energy vacuum energy density and pressure in Einstein's field equations, the cosmological constant problem is solved without the need for supersymmetry or extra dimensions. This is a novel and elegant solution that warrants further investigation.

In conclusion, this paper presents a thought-provoking and innovative approach to the cosmological constant problem by utilizing charge conjugation invariance of the vacuum. It offers a potential solution that does not require additional theoretical constructs and could have significant implications for our understanding of the universe.