Semiclassical Quantum Gravity in Two and Four Dimensions

Abstract

While a full quantum theory of gravity is still non-existent, continuous effort over the last years has shown some of the properties which an eventually complete theory will have to possess. At present, what is called “semiclassical quantum gravity” refers to different approaches and approximations: i Q.F.T. in curved space-time, in which matter fields are quantised on classical gravitational backgrounds, one of the first important examples being the Hawking radiation by black holes; this is also of conceptual and practical interest in early Cosmology and Inflation. ii Semiclassical Einstein equations, in which quantised matter fields react back (through the expectation value of the energy-momentum tensor) on the gemetry (the so-called “back-reaction problem”); important problems being the resolution of the late time evolution of black holes due to the reaction of Hawking radiation, and the reaction of particle production in the early-time evolution of the Universe. iii Semiclassical approximation to the path integral of gravity and matter fields, developed in the context of euclidean gravity with instanton and partition function methods (Gibbons and Hawking), recently combined with the Wheeler-DeWitt equation of canonical quantisation and applied to Cosmology for the problem of initial conditions and the ground state (Hartle-Hawking wave function).