Aspects of gravitational scattering at Planckian energies

Abstract

The standard Model is a gauge field theory based on the gauge group. As for the standard theory of elementary particle interactions, gravitation remains negligible at the highest of energies accessible to present day accelerators. Is there a quantum version of general relativity? If so, can it be unified with the the other three forces of nature? If three fundamental forces can be unified as a single theory, then presumably gravity should also follow some unification scheme which is unknown so far. The energy scales relevant for the quantum gravitational regime has been examined in this thesis. The theme of this thesis constitutes the scattering of point particles interacting via gravitation. The kinematics of the gravitation could be characterized by the two Mandelstam variables; The primary concern is the role of gravity in the scattering process; It is noted that at Planckian c.m. energies gravity dominates over other long range forces and a systematic analysis of the gravitational scattering amplitude reflect, almost entirely, the physical phenomena taking place at that scale. Although point particles are modelled by appropriate black hole metrics, the physical situation envisaged here is not identical to the scattering of black holes. The wavefunction of A is always a free wave function in the lightcone variables. Due to the shift function the wave function picks up a phase factor on being hit by the shock wave. After elaborating the various ways of deriving the eikonal formula, several assumptions regarding the nature of the particles and the interactions between them are relaxed. It is observed that the electromagnetism interaction between dyons are comparable to gravity even at the Planck Scale.