A more or less well behaved quantum gravity Lagrangean in dimension 4

Abstract

In this article we try to give a simple Quantum Gravity Lagrangean that behaves quite well. Feynman calculus for unpolarized crosssections, and the diagrams involved, behave good. The action is renormalizable by dimension counting. It implies standard Einstein gravity for a massless graviton. Further investigations have to be done. 1. A More or Less Well Behaved Quantum Gravity Lagrangean in Dimension 4? Note the identity 1 D/ 2 = +R/ = +Rab [Γ,Γ] 4 using the Dirac or Clifford Algebra representation Γ = θ + θ∗a [θ] a ON basis on the tangent space Tp(X) over a point p and [θ ∗a] a raised ON basis on the cotangent space T ∗ p (X) over the same point p, just like in the notation of E. Cartan, who wrote the metric g in terms of the veilbeins eμ = θ a μ as gμν = e a μδabe b ν , δab the Kronecker delta, and We sometimes suppress a minus-sign or a imaginary unit i in the following. 58 E.B. Torbrand Dhrif D/ = Γ(∂μ + ωμ + Aμ) = Γ ∇a Γ = eμΓ . We thus also conclude θ∗D/ θ = θ∗( +R/ )θ = θ∗ θ +R with R the Ricci scalar. Here θ is the graviton or vierbein. Here we have suppressed a term, including a coupling constant, 16πG. Notice that this is the Hilbert-Einstein action SGravity,Einstein = ∫