= Four-dimensional Majorana bilinear interchange
{title2=$\bar\chi\gamma^{abc}\eta=\bar\eta\gamma^{abc}\chi$}
For Grassmann-odd four-dimensional <Majorana spinors>, choose $C^T=-C$ and $(\gamma^a)^T=-C\gamma^aC^{-1}$. Then $C\gamma^a$ is symmetric whereas $C\gamma^{abc}$ is antisymmetric. Swapping Grassmann components therefore changes the sign of a vector bilinear but preserves a three-gamma bilinear. Integration by parts and antisymmetry of the vector indices then make the two spinor variations of the quadratic <Rarita-Schwinger field> action equal. Commuting auxiliary spinors have different interchange signs.
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