TITLE:
Scattering Cross-Sections in Quantum Gravity—The Case of Matter-Matter Scattering
AUTHORS:
Christian Wiesendanger
KEYWORDS:
Renormalizable Quantum Gravity, Scattering Cross-Sections in Quantum Gravity, Gauge Theory of Volume-Preserving Diffeomorphisms
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.3,
February
27,
2015
ABSTRACT: Viewing
gravitational energy-momentum PGμ as equal by
observation, but different in essence from inertial energy-momentum PIμ naturally
leads to the gauge theory of volume-preserving diffeomorphisms of a
four-dimensional inner 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 provides a
non-trivial test of the gauge field theory of volume-preserving diffeomorphisms
as a quantum theory of gravity.