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We study the quantum constraints of a conformal invariant action for a scalar
field. For this purpose we briefly present a reformulation of the duality
principle advanced in [1] in the context of generally covariant quantum field
theory, and apply it to examine 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.
Invariance breaking is introduced by defining a preferred configuration
of dynamical variables in terms of the large scale characteristics of
the universe. It this configuration a close relationship between the quantum
constraints and the Einstein equations is established.
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