  We derive the interaction of fermions with a dynamical space-time based on
the postulate that the description of physics should be independent of the
reference frame, which means to require the form-invariance of the fermion
action under diffeomorphisms. The derivation is worked out in the Hamiltonian
formalism as a canonical transformation along the line of non-Abelian gauge
theories. This yields a closed set of field equations for fermions,
unambiguously fixing their coupling to dynamical space-time. We encounter, in
addition to the well-known minimal coupling, anomalous couplings to curvature
and torsion. In torsion-free geometries that anomalous interaction reduces to a
Pauli-type coupling with the curvature scalar via a spontaneously emerged new
coupling constant with the dimension of mass resp.\ inverse length. A
consistent model Hamiltonian for the free gravitational field and the impact of
its functional form on the structure of the dynamical geometry space-time is
discussed.
