U(3) version of the f-g theory

A U(3)-invariant generalization of the f-g theory of the strong and gravitational interactions is given. An invariant Lagrangian is formulated, which is shown to describe a U(3) nonet of spin-2 fields, and a procedure is presented whereby the fields acquire masses through interaction with the gravitational field. Invariant interactions of the spin-2 fields with matter fields of spin 0, 1, and onehalf are also constructed, using for the last of these a generalization of the vierbein and spin connection formalism of general relativity. Finally, the full equations of motion for the spin-2 fields are derived.