Pseudo-unitarity of the spinor Lorentz representation
= Pseudo-unitarity of the spinor Lorentz representation
{title2=$S^\dagger\gamma^0S=\gamma^0$}
The spinor Lorentz matrices preserve the indefinite form defined by $\gamma^0$: $S^\dagger\gamma^0S=\gamma^0$. This follows from the gamma-matrix adjoint identities for infinitesimal generators and extends to finite connected transformations. Consequently the <Dirac adjoint> transforms with $S^{-1}$, even though a boost matrix is not ordinarily unitary.