= Dirac spinor pseudo-unitarity
{c}
{title2=$S^\dagger\gamma^0S=\gamma^0$}
The generators in the <Spinor representation of the Lorentz group> satisfy $M^\dagger\gamma^0+\gamma^0M=0$, so the finite transformation preserves the indefinite form $S^\dagger\gamma^0S=\gamma^0$. This makes $\bar\psi\psi$ a <Lorentz scalar> through the <Dirac adjoint>. Boost generators are Hermitian rather than anti-Hermitian: a boost has eigenvalues $e^{\pm\eta/2}$ and is not unitary in the ordinary positive-definite component norm. Rotations are unitary. This component representation is distinct from the unitary <action> on the physical state space.
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