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**Hi all,**

I make someexercises in particle physics but I'm stuck in two problems related to Gamma matrices identities,

I make some

First: the Fermion propagator ## \frac {i } { /\!\!\!p - m} = i \frac { /\!\!\!p + m } { p^2 - m^2} ## So how ##/ \!\!\!\!p ^2 = p^2 ## ? Where ## /\!\!\!p = \gamma_\mu p^\mu ##.

I think ##/ \!\!\!\!p ^2 = \gamma_\mu p^\mu \gamma_\nu p^\nu =

\gamma_\mu p^\mu \gamma_\nu g^{\mu\nu} p_\mu = \gamma_\mu \gamma^\mu p^2 = 4 p^2 ##, so I got a factor 4 ! What's wrong here?

Second: It's related to the helicity operator, ## h= S . \bf{p} ## ( where S is 2 by 2 matrix, with ##\sigma^i ## on the diagonal ), that as mentioned in a reference as [arXiv:1006.1718], it commutes with the Dirac Hamiltonian ## H = \gamma^0 ( \gamma^i p^i + m ) ## equ. (3.3), due to Gamma matrices anticommutation relation, but this isn't clear for me at all..

Thanx

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