Quantum Gravity Momentum Representation and Maximum Invariant Energy

TL;DR

This paper develops a quantum gravity framework in momentum space, introducing a maximum invariant energy and showing finite vacuum energy and self-energy, with implications for high-frequency physics.

Contribution

It constructs a momentum space quantum gravity geometry with a maximum invariant energy, providing finite results for vacuum and particle self-energies.

Findings

Finite vacuum energy density and self-energy of charged particles.

Modified electromagnetic radiation and entropy densities at high frequencies.

Introduction of a maximum invariant momentum in quantum gravity.

Abstract

We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}. For a closed maximally symmetric momentum space with a constant 3-curvature, the volume of the p-space admits a cutoff with an invariant maximum momentum a. A Wheeler-DeWitt-type wave equation is obtained in the momentum space representation. The vacuum energy density and the self-energy of a charged particle are shown to be finite, and modifications of the electromagnetic radiation density and the entropy density of a system of particles occur for high frequencies.