Peskin p135 5.10

1. Jul 1, 2015

newgate

Hello,
I'm doing the calculation of the unpolarized cross section in peskin QFT and i am facing a little obstacle, after the calculation of two traces i get terms containing $g^{\mu \nu}.g_{\mu \nu}$ and my question is how to deal with them? does this product equal to a numerical value?
Thank you.

2. Jul 1, 2015

Orodruin

Staff Emeritus
Yes. Are youfamiliar with SR and tensor notation? Do you know what $g^{\mu\nu}g_{\nu\rho}$ would be?

3. Jul 1, 2015

newgate

I think it's equal to $\delta_{\rho}^{\nu}$.....

4. Jul 1, 2015

Orodruin

Staff Emeritus
Indeed, so what is the trace of the Kronecker delta?

5. Jul 1, 2015

newgate

4 but terms containing $g^{\mu \nu}.g_{\mu \nu}$ come after the calculation of traces!!
Thanks

6. Jul 1, 2015

Orodruin

Staff Emeritus
It comes after calculating the traces of gamma matrices whose indices generally are suppressed, this is a trace of the Lorentz indices.

7. Jul 1, 2015

newgate

Ok Orodrui thank very much :)

8. Jul 1, 2015

Orodruin

Staff Emeritus
Just be aware that generally there will be loads of indices and traces which are implicit in field theory (and in particular gauge theory). Lorentz indices, spinor indices, group indices, flavour indices, etc. They may not always be written out but implicit because writing them out explicitly would fill your pages with a mountain of indices.

9. Jul 1, 2015

newgate

Ok i'll keep that in mind :D Thank you