I recently learned "Renormalization" and "RG".

My textbook says "RG allows us to make sense of why a renormalized quantum field theory describe Nature." To me, it sounds like "RG justifies the renormalization process which looks somewhat mathematically strange and funny."

As far as I know, the renormalization is a procedure to tame the unwanted divergence by introducing counter terms. And by doing that we shift our bare (false) parameters to physical parameters. The parameter shift occurs because interactions change the properties of particles such as mass and charge.

And RG is about how the coupling constants (parameters) change with the scale of interest.

In summary

  1. RG is about the change (ie. flow) in parameters with the varying scale and

  2. renormalization is about shift from bare parameters to physical parametes resulting from interaction

I cannot see the relation between RG and rernomalization and how RG justifies the renormalization process.

And I want to know to which part in RG the renormalization procedure (canceling divergence with the counter terms) corresponds.

That is, what is the canceling the infinities in view of RG?

  • 2
    $\begingroup$ When shifting from bare to physical parameters you have to choose specific physical parameters values and these values depend on the scale. The renormalization group then relates the different choices of scale. $\endgroup$ – Diracology May 9 '18 at 12:54

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