Hermitizing matrix ($H{\gamma }^a=(H{\gamma }^a{)}^{†}$)

A Hermitizing matrix for a set of gamma matrices is an invertible Hermitian matrix $H$ satisfying ${\gamma }^{a†}=H{\gamma }^a{H}^{-1}$. Equivalently, each $H{\gamma }^a$ is Hermitian. It defines a covariant adjoint $\bar{\psi }={\psi }^{†}H$. If ${\gamma }^{\prime a}=M{\gamma }^a{M}^{-1}$, then $H^{\prime }=M^{-†}H{M}^{-1}$ has the same property. In a standard Lorentzian Dirac basis, $H={\gamma }^0$ is a conventional choice.