= Discrete symmetries of a two-component Dirac field in three dimensions
{title2=$P:S_m\mapsto S_{-m},\quad T:S_m\mapsto S_{-m},\quad C:S_m\mapsto S_m$}
For <gamma matrices> $\gamma^0=\sigma_3$, $\gamma^1=i\sigma_1$, $\gamma^2=i\sigma_2$ and <Minkowski metric> $\operatorname{diag}(1,-1,-1)$, a one-axis spatial reflection acts with $\gamma^1$ on the two-component <Dirac field>. It preserves the <kinetic term> and reverses the <Dirac mass term>. <Time reversal> acts with $\gamma^2$ and includes conjugation of the operator coefficients; it has the same mass reversal. Their composition preserves a real mass. <Charge conjugation> can use $\psi_C=\gamma^1\psi^*$, because $\gamma^\mu\gamma^1=-\gamma^1\gamma^{\mu*}$. The mass bilinear is charge-conjugation even when <Grassmann field> exchange signs are included, and the kinetic action is invariant up to a boundary term. These statements concern the classical free <action>.
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