# Massless Dirac equation is Weyl covariant

Does somebody know how to show that the following equation is Weyl invariant?

$$\gamma^ae_a^\mu D_\mu \Psi=0$$

where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant derivative. Under a Weyl transformation the metric changes as $g^{'}_{\mu\nu}=\Omega^2g_{\mu\nu}$, with $\Omega$ positive function. In particular is to me not clear how spinors (and $D_\mu \Psi$) transform.

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Discussion here beginning at page 81 might be useful to you. –  twistor59 Jan 19 '13 at 21:40