= Majorana Grassmann bilinear interchange
{c}
{title2=$\bar\chi\epsilon=\bar\epsilon\chi$}
For Grassmann-odd spinors in two dimensions with $\bar\psi=\psi^TC$, $C^T=-C$ and $(\gamma^\mu)^TC=-C\gamma^\mu$, moving components past each other gives $\bar\chi\epsilon=\bar\epsilon\chi$ and $\bar\chi\gamma^\mu\gamma^\nu\epsilon=\bar\epsilon\gamma^\nu\gamma^\mu\chi$. The transpose of a two-gamma product reverses its order; the Grassmann sign and the antisymmetry of $C$ cancel. For $\delta\psi=B\gamma^\mu\partial_\mu X\epsilon$, this also gives $\delta\bar\psi=-B\bar\epsilon\gamma^\mu\partial_\mu X$. These identities fix the boundary variation in <worldsheet supersymmetry>; commuting spinors would not obey the same interchange rule.
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