Two-dimensional quantum gravity in Minkowski space

Abstract

We study exactly soluble models of gravity in two-dimensional Minkowski space. It is argued that an interpretation of these models as causal unitary quantum mechanics is possible only if we work in a Fock space of two-dimensional universes. The argument is general and should be valid for any generally covariant Minkowski field theory which contains the metric as a dynamical variable. It depends only on global time reparametrization invariance. We conjecture that the local time reparametrization invariance of theories of extended objects actually requires that the second quantized theory of such objects be an interacting Universal Field Theory, i.e. that it must contain wormhole processes.