Sorry for spamming the forums, but one last question for today!(adsbygoogle = window.adsbygoogle || []).push({});

If

[tex]\Sigma^k=\frac{i}{2} \epsilon_{kij} [\gamma^i , \gamma^j][/tex]

where [A,B]=AB-BA

Why does [tex]{\Sigma^1=2i \gamma^2\gamma^3[/tex] (that's what my notes say, anyway)

I think it should equal:

[tex]\Sigma^1=\frac{i}{2}\epsilon_{123}[\gamma^2,\gamma^3] + \frac{i}{2}\epsilon_{132}[\gamma^3,\gamma^2] [/tex]

[tex] = \frac{i}{2}(+1)}[\gamma^2,\gamma^3] + \frac{i}{2}(-1)(-[\gamma^2,\gamma^3])[/tex]

[tex] =i[\gamma^2,\gamma^3] [/tex]

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# Levi Civita and commutators

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