1208.2338 (Christian Wiesendanger)

Scattering Cross-Sections in Quantum Gravity - the Case of Matter-Matter
Scattering    [PDF]

Christian Wiesendanger

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space. To analyse scattering in this theory the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This is a further indication that the gauge field theory of volume-preserving diffeomorphisms can be viewed as a quantum theory of gravity

View original: http://arxiv.org/abs/1208.2338