2005/08/31 by G. Mack, Gerhard Mack, Thorsten Prüstel +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1140/epjc/s2005-02443-2
published as Eur.Phys.J.C46:255-267,2006 · 33 pages
arxiv created 2005/10/24 · openalex publication_date 2006/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In gauge theories parallel transporters (PTs) U(C) along paths C play an important role. Traditionally they are unitary or pseudoorthogonal maps between vector spaces. We propose to abandon unitarity of parallel transporters and with it the a priori assumption of metricity in general relativity. A *-operation on parallel transporters serves as a substitute for it, and this *-operation is proven to be unique on group theoretical grounds. The vierbein and the spin connection appear as distinguishable parts of a single de Sitter gauge field with field strength F. The action takes the form (3)/(16πGΛ)∫ tr(F \wedge F i γ5) and both the Einstein field equations with arbitrarily small but nonvanishing cosmological constant Λ and the condition of vanishing torsion are obtained from it. The equation of motion for classical massive bodies turns out to be de Sitter covariant.