A new perspective on quantum gravity

Abstract

We present a new approach to quantum gravity whose basic idea is a confluence of four elements: 1) the possibility of working with manifolds on three different levels of abstraction, which are i) a general differentiable manifold; ii) an affmely connected manifold; iii) a manifold with a metric structure; 2) Carmeli’s SL(2, C) gauge theory formulation of General Relativity, which implies the possibility that the quantities that need to be quantized are spinor potential and/or fields, rather than the components of the metric tensor; 3) the formulation of Carmeli’s theory on affinely connected, rather than metric space-time; and, finally, 4) the discovery of the possibility to have a Lagrangian formulation of Carmeli’s theory on general differentiable manifolds. In the suggested approach, then, the quantized quantities are not the components of the metric tensor but quantities that arise naturally in the SL(2, C) gauge theory, and the problem of the absence of a space-time with a given structure as a background does not arise, because the quantization is based on a Lagrangian defined over a general differentiable manifold.