Casimir's trick / Evaluating trace

[BookWei]

Hi all, I am working on a project at the moment, and I have to evaluate the trace by using the Casimir's trick.
The trace form is
$$Tr[(\displaystyle{\not} P +M_{0})\gamma^{\mu}(\displaystyle{\not} P^{'} +M^{'}_{0})(\displaystyle{\not} p^{'}_{1} +m^{'}_{1})\gamma^{\nu}(\displaystyle{\not} p_{1} +m_{1})]$$
I have no idea how can I simplify this form by using Casimir's trick.
Can somebody help me solve this problem?
Many thanks!

 

[nrqed]

Hi all, I am working on a project at the moment, and I have to evaluate the trace by using the Casimir's trick.
The trace form is
$$Tr[(\displaystyle{\not} P +M_{0})\gamma^{\mu}(\displaystyle{\not} P^{'} +M^{'}_{0})(\displaystyle{\not} p^{'}_{1} +m^{'}_{1})\gamma^{\nu}(\displaystyle{\not} p_{1} +m_{1})]$$
I have no idea how can I simplify this form by using Casimir's trick.
Can somebody help me solve this problem?
Many thanks!

Just expand the products and then use that the trace of a sum is the sum of the traces. Then you will have a bunch of traces of monomials. For each you may use the identities (see for example the wikipedia entry on gamma matrices)

 

[BookWei]

Just expand the products and then use that the trace of a sum is the sum of the traces. Then you will have a bunch of traces of monomials. For each you may use the identities (see for example the wikipedia entry on gamma matrices)

Thank you so much.