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Adjoint Spinor

Because the combination $\psi^\dagger\gamma_0$ occurs so often, we define


\begin{displaymath}
\overline{\psi}(x) \equiv \psi^\dagger\gamma_0,
\end{displaymath} (5.162)

where $\overline{\psi}(x)$ is the adjoint spinor.

Its Lorentz transformation properties are


$\displaystyle \psi^\prime(x^\prime)$ $\textstyle =$ $\displaystyle S\psi(x)$  
$\displaystyle \psi^{\prime^\dagger}(x^\prime)$ $\textstyle =$ $\displaystyle \psi^\dagger(x)S^\dagger =
\psi^\dagger(x)\gamma_0S^{-1}\gamma_0$  
$\displaystyle \psi^{\prime^\dagger}(x^\prime)\gamma_0$ $\textstyle =$ $\displaystyle \overline{\psi}^\prime(x^\prime) = \overline{\psi}(x) S^{-1}.$ (5.163)



Douglas M. Gingrich (gingrich@ ualberta.ca)
2004-03-18