Abstract
The minimal and nonminimal interactions between the gravitational and tensor meson fields are studied by performing a canonical analysis, starting from a Lagrangian which verifies the Fierz-Pauli condition and meaning by minimal interaction terms coming from the replacement of the usual derivatives by the Riemannian covariant derivatives in the flat Lagrangian. The nonminimal interaction, however, takes into account terms coupling first-order derivatives of the gravitational field with mesonic currents. It is very well known that the assumptions of minimal gravitational interaction for the scalar mesons, photons and massive spin-1/2 fermions give consistent theories. However, in the present work, it is shown that both coupling schemes are inconsistent.
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