- #1

tomdodd4598

- 138

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- TL;DR Summary
- How is coupling renormalisation done in general?

Hey there!

I am still rather new to renormalising QFT, still using the cut-off scheme with counterterms, and have only looked at the φ^4 model to one loop order.

In that model, we renormalise with a counterterm to the one-loop four-point 1PI diagram at a certain energy scale.

Do I simply, in the case of φ^3, do roughly the same, that is renormalise with a counterterm to the one-loop

The reason I ask is because I was confused by the renormalisation of the electric charge in QED, which involved looking at the photon propagator rather than the interaction vertex as I had originally expected...

This leads me to the overarching question: is there a generic way to know which diagrams/processes to look at in order to renormalise interaction coupling constants, and does the fact of whether a coupling is dimensionless or not, or whether the single-vertex tree-level interaction can actually conserve energy and momentum (not the case in φ^3 or QED) affect this in any way?

Thanks in advance!

I am still rather new to renormalising QFT, still using the cut-off scheme with counterterms, and have only looked at the φ^4 model to one loop order.

In that model, we renormalise with a counterterm to the one-loop four-point 1PI diagram at a certain energy scale.

Do I simply, in the case of φ^3, do roughly the same, that is renormalise with a counterterm to the one-loop

*three-point*1PI diagram at a certain energy scale?The reason I ask is because I was confused by the renormalisation of the electric charge in QED, which involved looking at the photon propagator rather than the interaction vertex as I had originally expected...

This leads me to the overarching question: is there a generic way to know which diagrams/processes to look at in order to renormalise interaction coupling constants, and does the fact of whether a coupling is dimensionless or not, or whether the single-vertex tree-level interaction can actually conserve energy and momentum (not the case in φ^3 or QED) affect this in any way?

Thanks in advance!