Simplifying expression with gamma matrix and slashes

[besprnt]

I am trying to simplify the expression
$\not p \gamma^\mu \not p.$
I believe the answer should be
$- \frac{1}{2} \gamma^\mu p^2,$
but I am not sure.

Tom

 

[WannabeNewton]

$\gamma^{\nu}\gamma^{\mu}\gamma^{\lambda} = g^{\mu\nu}\gamma^{\lambda} + g^{\mu\lambda}\gamma^{\nu} - g^{\nu \lambda}\gamma^{\mu} - i\epsilon^{\delta\nu\mu\lambda}\gamma_{\delta}\gamma^5 \\ \Rightarrow \not p \gamma^{\mu}\not p = 2p^{\mu}\not p - \gamma^{\mu} p^2$.

 

[besprnt]

Thanks.