Quantum gravity momentum representation and maximum energy

Abstract

We use the idea of the symmetry between the spacetime coordinates [Formula: see text] and the energy–momentum [Formula: see text] in quantum theory to construct a momentum space quantum gravity geometry with a metric [Formula: see text] and a curvature tensor [Formula: see text]. For a closed maximally symmetric momentum space with a constant 3-curvature, the volume of the [Formula: see text]-space admits a cutoff with an invariant maximum momentum [Formula: see text]. 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.