Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem

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.

arXiv comment15 pages, Latex file, no figures. Typos corrected. To be published in Physics Letters B

References in corpus (15)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Supernova Limits on the Cosmic Equation of State
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Quantum Entanglement of Moving Bodies
• Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
• Scalar Quantum Field Theory with Cubic Interaction
• PT-Symmetric Quantum Electrodynamics
• The C Operator in PT-Symmetric Quantum Field Theory Transforms as a Lorentz Scalar

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• Quantum fields, cosmological constant and symmetry doubling
• A way to get rid of cosmological constant and zero point energy problems of quantum fields through metric reversal symmetry
• A symmetry for vanishing cosmological constant
• A Causal Alternative to Feynman's Propagator
• Cosmological Consequences of Anti-gravitation
• Localization of particles in quantum field theory
• Static Scalar Field Solutions in Symmetric Gravity
• Mechanism for Resolving Gauge Hierarchy and Large Vacuum Energy