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Quantum Gravity Momentum Representation and Maximum Invariant Energy

We use the idea of the symmetry between the spacetime coordinates x^μand the energy-momentum p^μin quantum theory to construct a momentum space quantum gravity geometry with a metric s_{μν} and a curvature P^λ_{μνρ}. 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.