# Casimir's trick / Evaluating trace

• I
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!

Related High Energy, Nuclear, Particle Physics News on Phys.org
nrqed
Homework Helper
Gold Member
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)

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.