= Grassmann variation of a chiral Majorana mass term
{c}
{title2=$i\not\partial\psi-m^*\psi^c=0,\quad i\not\partial\psi^c-m\psi=0$}
For anticommuting components and an antisymmetric numerical matrix $A$, $\delta(\psi^TA\psi)=2\delta\psi^TA\psi$: move the second varied field past the first and use $A^T=-A$. Applying this to $C^{-1}$ and to $C$ cancels the factor $1/2$ in $\mathcal L=\bar\psi i\not\partial\psi+\tfrac12(m\psi^TC^{-1}\psi-m^*\bar\psi C\bar\psi^T)$. Varying the <Dirac adjoint> gives the first displayed equation. Integration by parts in the spinor variation gives $i\gamma^{\mu T}\partial_\mu\bar\psi^T+mC^{-1}\psi=0$; multiplication by $C$ gives the second. Squaring the coupled equations yields $(\Box+|m|^2)\psi=0$, so the physical <Majorana fermion> mass is $|m|$.
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