There is a step that bothers me in my book (Ryder) on QFT and I can't seem to figure it out. It concerns the (spatial) rotation of the spatial part of the Dirac four current:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\bar{\psi} \gamma \psi [/tex]

The crucial step here is

[tex]\frac{1}{4}(\vec{\sigma} \cdot \vec{\theta}) \vec{\sigma}(\vec{\sigma} \cdot \vec{\theta}) = -\vec{\theta} \times \vec{ \sigma} [/tex]

With [itex]\vec{\theta}[/tex] the (infinitesimal) rotation and [itex]\vec{\sigma}[/tex] the vector consiting of the three Pauli matrices.

I tried writing it in tensor notation and using the commutation reltaions as in the supplied tip, but I can't figure it out... Can anybody show me this?

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# Rotating Dirac particle current

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