Abstract
We analyze the relationship for spinor theories in a gravitational background between the invariances of the full non-linear theory (general coordinate transformations and local vierbein rotations) and the behaviour of matrix elements ( S-matrix elements or matrix elements of composite operators) when an external graviton is longitudinal Special emphasis is laid on the massless Rarita-Schwinger field. Here we find a connection between fermionic gauge invariance and invariance under the non-linear transformations. Consequently the one-loop axial vector current here only possesses the invariances of the non-linear theory, as well as the property of having matrix elements that vanish for longitudinal external gravitons, in a completely covariant gauge.
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