Generally covariant quantum field theory and scaling limits

Abstract

The formulation of a generally covariant quantum field theory is described. It demands the elimination of global features and a characterization of the theory in terms of the allowed germs of families of states. A simple application is the computation of counting rates of accelerated idealized detectors. As a first orientation we discuss here the consequences of the assumption that the states have a short distance scaling limit. The scaling limit at a point gives a reduction of the theory to tangent space. It contains kinematical information but not the full dynamical laws. The reduced theory will, under rather general conditions, be invariant under translations and under a proper subgroup of the linear transformations in tangent space. One interesting possibility is that it is invariant under SLR(4). Then the macroscopic metric must evolve as a cooperative effect in finite size regions. The other natural possibility is that each family (coherent folium) of states defines a microscopic metric by the scaling limit and the tangent space theory reduces to a theory of free massless fields in a Minkowski space. Irrespective of the assumption of a scaling limit we show that the theory can be constructed from strictly local information.