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

• newgate
In summary, the conversation is discussing the calculation of the unpolarized cross section in Peskin QFT and how to deal with terms containing ##g^{\mu \nu}.g_{\mu \nu}##. The product is equal to a numerical value, specifically ##\delta_{\rho}^{\nu}##, and it comes after calculating the traces of gamma matrices with suppressed indices. There are various indices and traces that are implicit in field theory and may not always be written out explicitly.
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.

newgate said:
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}##...

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

newgate said:
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.

Ok Orodrui thank very much :)

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.

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

## What is a cross section in Peskin QFT?

A cross section in Peskin QFT refers to the probability that a specific interaction or process will occur between two particles. It is calculated using the Feynman diagrams and involves the use of mathematical techniques such as perturbation theory.

## How is the cross section calculated in Peskin QFT?

The cross section is calculated using the Feynman rules and perturbation theory in Peskin QFT. This involves breaking down the interaction into smaller parts, calculating the amplitudes for each part, and then combining them to obtain the final cross section.

## What is g^μν.g_μν in the context of cross section calculation in Peskin QFT?

In cross section calculation in Peskin QFT, g^μν.g_μν refers to the contraction of the metric tensor, which is used to describe the geometry of spacetime. It is often used to simplify equations and is an important concept in quantum field theory.

## How do I deal with g^μν.g_μν in cross section calculation in Peskin QFT?

To deal with g^μν.g_μν in cross section calculation in Peskin QFT, you can use the properties and identities of the metric tensor to simplify the equations. This involves taking into account the symmetry and invariance of the metric tensor and using it to rewrite expressions in a more manageable form.

## What are some common challenges in dealing with g^μν.g_μν in cross section calculation in Peskin QFT?

Some common challenges in dealing with g^μν.g_μν in cross section calculation in Peskin QFT include understanding the properties and identities of the metric tensor, keeping track of indices, and correctly applying the Feynman rules. It is important to practice and have a good understanding of the basics of quantum field theory to effectively deal with g^μν.g_μν in cross section calculation.

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