= Infinitesimal transformation of a Dirac field
{title2=$\delta\Psi=-\omega^\mu{}_{\nu}x^\nu\partial_\mu\Psi-\tfrac i4\omega_{\mu\nu}\sigma^{\mu\nu}\Psi$}
For $\Lambda=1+\omega$ with antisymmetric lowered parameters, the spin matrix is $S=1-(i/4)\omega_{\mu\nu}\sigma^{\mu\nu}$, where $\sigma^{\mu\nu}=(i/2)[\gamma^\mu,\gamma^\nu]$. At transformed coordinates this is the full component transformation. At fixed coordinates an additional orbital term $-\omega^\mu{}_{\nu}x^\nu\partial_\mu\Psi$ appears.
Back to article page
