= Charge-conjugate field
{title2=$\psi^c=C\bar\psi^T$}
The charge-conjugate field of a <fermion> field transforms in the complex-conjugate internal <group representation>. With a compatible <Dirac adjoint> and <charge conjugation> matrix convention it is $\psi^c=C\bar\psi^T$, up to a conventional constant phase. In four spacetime dimensions <charge conjugation> exchanges the <chirality> of the field; a right-handed quark can therefore be represented by a left-handed conjugate field when listing chiral unified matter. In two-dimensional Minkowski spacetime, <charge conjugation> can instead preserve <chirality>, permitting a <Majorana-Weyl spinor>.
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