I stumbled across the Wikipedia article on coupling constants  and didn't quite unterstand, what the paragraph on running couplings is trying to express.
It relates the virtual particles taking part in some scattering process and the apparent violation of energy conservation to the uncertainty principle of energy and time and concludes: “The previous remark only applies to some formulations of quantum field theory, in particular, canonical quantization in the interaction picture. In other formulations, the same event is described by ‘virtual’ particles going off the mass shell. Such processes renormalize the coupling and make it dependent on the energy scale, $\mu$, at which one observes the coupling.“
Now there are two things, that I don't understand:
- How can canonical quantization in the interaction picture circumvent the introduction of a running coupling?
- How does the connection to the uncertainty principle arise (at least heuristically, as it says)?