| Abstract: | We study the quantum constraints of a conformalinvariant action for a scalar field. For this purpose webriefly present a reformulation of the duality principleadvanced earlier in the context of generally covariant quantum field theory, and apply it toexamine the finite structure of the quantum constraints.This structure is shown to admit a dimensional coupling(a coupling mediated by a dimensional coupling parameter) of states to gravity. Invariancebreaking is introduced by defining a preferredconfiguration of dynamical variables in terms of thelargescale characteristics of the universe. In thisconfiguration a close relationship between the quantumconstraints and the Einstein equations isestablished. |
