Chirality matrix
= Chirality matrix
{title2=$\gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3$}
= Gamma five matrix
{synonym}
With metric $(+---)$, the chirality matrix has $(\gamma^5)^2=1$ and anticommutes with each <gamma matrix>. Its eigenspaces define <chirality>; $P_L=(1-\gamma^5)/2$ and $P_R=(1+\gamma^5)/2$ are the corresponding projectors. These identities follow directly by moving a <gamma matrix> through the ordered product and using the <Clifford algebra>.