Conformal invariance in gauge theories. III. Linear gravitation

The results of the first two parts of the present study are generalized to the case of nonlinear gravitation. Under the assumption that the gauge tensor field of second rank transforms in accordance with a nonprincipal representation of the conformal group it is found that the conformally invariant two-point functions of this field have nonzero transverse part, and a nondegenerate conformally invariant Lagrangian is also constructed. It is shown that in the gauge-invariant sector this theory is identical with ordinary renormalizable linear gravitation. The global symmetry of the effective Lagrangian, which can be used to separate the subspace of transverse states and derive a Ward identity, is discussed.