Coupling of Quantum Fields to Classical Gravity

Abstract

We consider ensembles on configuration space that consist of quantum fields which interact with and are the source of a classical gravitational field. These are hybrid systems where gravity remains classical while matter is described by quantized fields. There are some well known arguments in the literature which claim that such models are not possible. However, an examination of the most prominent ones, that are detailed enough to allow scrutiny, indicates that the hybrid models considered here are not excluded by any of the consistency arguments. We illustrate the approach with two examples. Our first example is a cosmological model. We consider the case of a closed Robertson–Walker universe with a massive quantum scalar field and solve the equations using a particular ansatz which selects a highly non-classical solution, one in which the scale factor of the Robertson–Walker universe is restricted to discrete values as a consequence of the interaction of the classical gravitational field with the quantized scalar field. We discuss this cosmological model in two approximations, that of a minisuperspace model and that of a midisuperspace model. Our second example concerns black holes. We consider CGHS black holes and show that we recover Hawking radiation from the equations that describe a hybrid system consisting of a classical CGHS black hole in a collapsing geometry interacting with a quantized scalar field. We also show that the hybrid model provides a natural resolution to the well known problem of time in quantum gravity. Show more