A Hamiltonian approach to quantum gravity

Abstract

We explore the idea that gravitational interaction can be described by instantaneous inter-particle potentials. This idea is in full accord with relativistic quantum theory. In particular, it resembles the ``dressed particle'' approach to quantum electrodynamics. Although the complete non-perturbative of this theory is yet unknown, one can reasonably guess its form in low perturbation orders and in the (1/c)^2 approximation. We suggest a relativistic energy operator, which in the classical limit reduces to the Einstein-Infeld-Hoffmann Hamiltonian for massive particles and correctly describes the effects of gravity on photons, including the light bending, the Shapiro delay, the gravitational time dilation and the red shift. The causality of this approach is briefly discussed.