Classical and quantum gravity from relativistic quantum mechanics

Abstract

It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group. Representations of the Poincar\'e group are characterised by fixed eigenvalues of two Casimir operators corresponding to a fixed mass and a fixed angular momentum. In multi-particle systems (of massive spinless particles), fixing these eigenvalues leads to correlations between the particles. In the quasi-classical approximation of large quantum numbers, these correlations take on the structure of a gravitational interaction described by the field equations of conformal gravity. A theoretical value of the corresponding gravitational constant is calculated. It agrees with the empirical value used in the field equations of general relativity.