(adsbygoogle = window.adsbygoogle || []).push({}); Dirac Matrix Property? Possible Book mistake? Derive KG from Dirac

I got a copy of QFT demystified and on pg. 89 he says he can write [itex]\gamma_{\nu} \gamma^{\mu} = g_{\nu \sigma} \gamma^{\sigma} \gamma^{\mu} = g_{\nu \sigma} \frac{1}{2} (\gamma^{\sigma} \gamma^{\mu} + \gamma^{\mu} \gamma^{\sigma}) [/itex]

and i am trying to figure out why this is because the only reason I could see why it's true is if [itex]\gamma^{\mu} \gamma^{\nu} = \gamma^{\nu} \gamma^{\mu}[/itex] which for the love of my brain I can't figure out why that would be true, I'm pretty sure it's not. Is this a book mistake. For reference what he is doing is deriving the KG equation starting from Dirac.

on another note, regardless of the answer what i am actually looking for is a derivation of the kg equation starting from dirac, or perhaps the other way around. if someone can point me to that, that is a fine answer as well.

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# Dirac Matrix Property? Possible Book mistake?

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