  The natural constraints for the weak-field approximation to composite
gravity, which is obtained by expressing the gauge vector fields of the
Yang-Mills theory based on the Lorentz group in terms of tetrad variables and
their derivatives, are analyzed in detail within a canonical Hamiltonian
approach. Although this higher derivative theory involves a large number of
fields, only few degrees of freedom are left, which are recognized as selected
stable solutions of the underlying Yang-Mills theory. The constraint structure
suggests a consistent double coupling of matter to both Yang-Mills and tetrad
fields, which results in a selection among the solutions of the Yang-Mills
theory in the presence of properly chosen conserved currents. Scalar and
tensorial coupling mechanisms are proposed, where the latter mechanism
essentially reproduces linearized general relativity. In the weak-field
approximation, geodesic particle motion in static isotropic gravitational
fields is found for both coupling mechanisms. An important issue is the proper
Lorentz covariant criterion for choosing a background Minkowski system for the
composite theory of gravity.
