Geometry of Scattering at Planckian Energies

TL;DR

This paper introduces a geometric approach to describe scattering processes at Planckian energies using a topological field theory derived from a truncated Einstein action, emphasizing differential forms and topological invariants.

Contribution

It provides an alternative geometric derivation of Verlinde's topological field theory applicable to high-energy scattering near the Planck scale, using standard geometrical objects.

Findings

Derivation of a topological invariant for Planckian energy scattering

Use of differential forms in the formulation

Connection to a truncated Einstein action

Abstract

We present an alternative derivation and geometrical formulation of Verlinde topological field theory, which may describe scattering at center of mass energies comparable or larger than the Planck energy. A consistent trunckation of 3+1 dimensional Einstein action is performed using the standard geometrical objects, like tetrads and spin connections. The resulting topological invariant is given in terms of differential forms.