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I'm currently studying Griffith's Intro to Elementary Particles and in chapter 7 about QED, there's one part of an operation on tensors I don't follow in applying Feynman's rules to electron-muon scattering :

## \gamma^\mu g_{\mu\nu} \gamma^\nu = \gamma^\mu \gamma_\mu##

My teacher spent very little time on tensors and I'm really not sure 1) what's the difference between ##\gamma^{\mu\nu}## and ##\gamma_{\mu\nu}##, 2) why is the second ##\gamma##'s indice switched from ##\nu## to ##\mu## (and was also lowered).

Besides, I'm still strugling to understand the general difference between lowered and raised indices (e.g. : why I'm never seeing ##\gamma_\mu^\nu##, but other tensors are written that way). In Griffith's electrodynamics, the author says that in ##\Lambda_\mu^\nu##, it is ##\mu## that represents lines and ##\nu## that represents columns. However, this isn't consistent with everything I'm seeing on tensors.

Thanks!

Alex

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# I Metric tensor : raising/lowering indices

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