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Ok, after posting this question I have been trying to solve this and finally did, so I am posting the answer. Just one identity is enough and that is: $$ \gamma^\mu\gamma^\nu\gamma^\lambda = g^{\mu\nu}\gamma^\lambda + g^{\nu\lambda}\gamma^\mu - g^{\mu\lambda}\gamma^\nu + i \epsilon^{\sigma\mu\nu\lambda} \gamma_\sigma\gamma^5 $$ And a few basic ...


Scrednicki's textbook chapter 50. is about spinor helicity techniques. He uses a different notation though. Fierz identity is one of the problems.


There isn't a good definition of chirality in (2+1)D or any other odd dimension. This is because the $\gamma_5$ matrix can't be defined usefully in a Clifford algebra with an odd number of generators. For instance try to define $\gamma_5 = \gamma^0\gamma^1\gamma^2$. This commutes (not anti-commutes) with $\gamma^0,\gamma^1,\gamma^2$ and thus commutes with ...

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