I would like to take the trace over spinorial indices of the following expression:(adsbygoogle = window.adsbygoogle || []).push({});

[tex](\gamma_{\mu}\gamma^{0})_{\alpha}^{\beta}=(\gamma_{\mu})_{\alpha}^{\gamma}(\gamma^{0})_{\gamma}^{\beta}[/tex].

How do I go about doing this? I reckon I could expand the trace out (let's say I want to do this in 4D) and use a particular representation of the algebra of the gammas, but is there a representation-independent way of doing it?

Also, it confuses me that in the equation above, if one traces over it, it becomes [itex](\gamma_{\mu})_{\alpha}^{\beta}(\gamma^{0})_{\beta}^{\alpha}[/itex], where the beta index is summed over properly according to the spinor northwest-southeast convention, while the alphas aren't. Is this a problem?

I guess my main question is, how do you take a trace over spinor indices?

Thanks

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# How to trace over spinor indices?

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