Why does physics change along the RG trajectory if physical quantities are μ-independent?

[anthony2005]

First a little intro.

The process of renormalization introduces in a QF theory a renormalization scale μ. Physical quantities do not depend on it, as a change of μ comes along with the change of the coupling g(μ) according to the RG law.

But why then the physics can change so drastically along the RG trajectory? For instance, why asymptotic freedom in QCD is attributed to the unphysical ( μ,g(μ) ) RG behaviour? The μ is not introduced as the physical energy of a given process.

Thanks

 

[Avodyne]

Physics changes with the physical energy scale, not with μ. But if you choose μ near the relevant physical energy scale, and g(μ) happens to be small, then low orders of perturbation theory will give a good description of physics at that physical energy scale. If not, not.