= Opposite intrinsic parities of a Dirac particle and antiparticle
In the <Dirac representation of the gamma matrices>, the <parity symmetry in quantum field theory> action $\psi_P(x)=\gamma^0\psi(x_P)$ and the <charge conjugation> action $\psi_C=i\gamma^2\psi^*$ obey $(\psi_P)_C(x)=-\gamma^0\psi_C(x_P)$, since $\gamma^0$ is real and anticommutes with $\gamma^2$. At rest, positive-frequency <Dirac spinors> have nonzero upper components and negative-frequency <Dirac spinors> have nonzero lower components; they are respectively $+1$ and $-1$ eigenvectors of $\gamma^0$. With the common conventional real intrinsic-parity phase, particle and antiparticle therefore have opposite <intrinsic parity>. The overall sign is conventional, whereas their relative sign is fixed.
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