- #1

MichaelJ12

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- TL;DR Summary
- Trying to find out how a certain quantity transforms under Lorentz transformations.

I am trying to understand the last block of equations in the picture (after 3.31). In the first line of that block, he transforms the spinor ##\psi## which I have no problem with. What I have a problem with is the ##\gamma ^{\mu} \partial _{\mu}##. They form a Lorentz scalar, so they should not change as a whole, because ##\gamma ^{\mu} \partial _{\mu} \to \Lambda ^\mu _{\; \alpha} \gamma ^{\alpha} (\Lambda ^{-1}) ^\nu _{\; \mu} \partial _{\nu} = \gamma ^{\mu} \partial _{\mu} ##. Instead, he only transforms the derivative in this way: ##\partial _{\mu} \to (\Lambda ^{-1}) ^\nu _{\; \mu} \partial _{\nu} ##. My question is why doesn't he transform the gamma matrices as well? They have a Lorentz index too.

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