= Worldsheet chirality and propagation direction
{title2=$\psi_+=F(\tau-\sigma),\ \psi_-=G(\tau+\sigma)$}
In signature $(-,+)$, choose real <gamma matrices> $\gamma^0=\bigl(\begin{smallmatrix}0&-1\\1&0\end{smallmatrix}\bigr)$, $\gamma^1=\bigl(\begin{smallmatrix}0&1\\1&0\end{smallmatrix}\bigr)$ and $\gamma_*=-\gamma^0\gamma^1$. The <Dirac equation> then gives $(\partial_\tau+\partial_\sigma)\psi_+=0$ and $(\partial_\tau-\partial_\sigma)\psi_-=0$. Positive <chirality> is right-moving and negative <chirality> is left-moving in this orientation. Reversing the definition of $\gamma_*$ exchanges the labels without changing the physics.
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