Cross Section Calc. in Peskin QFT - How to Deal with g^μν.g_μν?

[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.

 

[Orodruin]

does this product equal to a numerical value?

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

 

[newgate]

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

 

[Orodruin]

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

 

[newgate]

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

 

[Orodruin]

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

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

 

[newgate]

Ok Orodrui thank very much :)

 

[Orodruin]

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.

 

[newgate]

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