I didn't quite know where to put this one.

I'll get the definitions in here first:

$\displaystyle \gamma ^0 = \left ( \begin{matrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{matrix} \right )$

$\displaystyle \gamma ^1 = \left ( \begin{matrix}0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \end{matrix} \right )$

$\displaystyle \gamma ^2 = \left ( \begin{matrix}0 & 0 & 0 & -i \\ 0 & 0 & i & 0 \\ 0 & i & 0 & 0 \\ -i & 0 & 0 & 0 \end{matrix} \right )$

$\displaystyle \gamma ^3 = \left ( \begin{matrix}0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{matrix} \right )$

$\displaystyle \eta = \left ( \begin{matrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{matrix} \right )$

My question is this: How do I evaluate $\displaystyle Tr \left [ \gamma ^{\mu} ~ \gamma ^{\sigma} ~ \gamma ^{\lambda} ~ \gamma ^0 \right ] $

The only other information I have that might be useful is the anti-commutator

$\displaystyle \left \{ \gamma ^{\mu} ,~ \gamma ^{\sigma} \right \} = \gamma ^{\mu} ~ \gamma ^{\sigma} + \gamma ^{\sigma} ~ \gamma ^{\mu} = 2~ \eta ^{\mu \sigma}$

Thanks!

-Dan