Are running couplings distinctively 'quantum'?

[metroplex021]

As is well known, the charges through which particles interact scale with the energy in QFT. What I was wondering is: can we say that this is a peculiarly 'quantum' phenomenon (or maybe, quantum-relativistic)? Is there a reason why it wouldn't be the case in a classical universe, for example?

Just a rainy afternoon question... any thoughts or musings would be appreciated!

 

[ChrisVer]

I don't understand your question.
the running coupling constants appear in the framework of quantum field theory. So they are quantum.
If by classical you mean the tree level interactions of classical fields, then yes the running of the coupling constant is a quantum effect appearing from higher order diagram corrections.

 

[The_Duck]

Yes, as ChrisVer says the running of the coupling in QFT comes from loop diagrams, and loop diagrams are inherently quantum mechanical because they represent the process of summing together the amplitudes of many different classical histories.

That said there are classical phenomena that are analogous in some ways. We call the running of the electric charge "vacuum polarization" because it is similar to polarization effects and charge shielding in classical dielectrics.

 

[metroplex021]

Yes, I appreciate that the running couplings appear in QFT. But -- as anyone who's benefited from reading Feynman knows -- derivation is not always the same thing as explanation. Is there a story, a gloss we can give on why the running of couplings is *distinctively* quantum?

 

[metroplex021]

OK: so is the idea here that the Callen-Symanzik equation governs renormalized coupling constants, and those things are only introduced in order to deal with divergent diagrams, which always include loops (and hence are intrinsically QMical)?

Thanks for reminding me of the analogy with dielectrics, The_Duck.

 

[haushofer]

In the end the running of the couplins is due to virtual states coming from the superposition principle and perturbation theory. So I would say yes.

 

[haushofer]

Yes, as ChrisVer says the running of the coupling in QFT comes from loop diagrams, and loop diagrams are inherently quantum mechanical because they represent the process of summing together the amplitudes of many different classical histories.

That said there are classical phenomena that are analogous in some ways. We call the running of the electric charge "vacuum polarization" because it is similar to polarization effects and charge shielding in classical dielectrics.

Can mass renorm. be understood in the same way, by the way?

 

[haushofer]

And, related to that, can this " vacuum polarization" -picture explain why the coupling increases with energy instead of decreases (antiscreening instead of screening?)

Without wanting to hijack this topic, of course. ;)

 

[ChrisVer]

I think it [vacuum polarization] explains why it's decreasing not increasing. It's more like the same charge is "expanded" in space...and so something going through it at high energies will see except for the positive charges the negative too.

 

[haushofer]

Maybe I'm mixing stuff up, I'll check.

 

[arivero]

In fact I had always thought that the "vacuum polarization picture" is the divulgative argument to explain running couplings in the Scientific American or similar newsjournals. It can be argued that it will be different for SU(3) that for U(1), so different runnings. And it is a quantum-relativistic picture, because the polarization is not of the "vacuum" but of the pairs particle-antiparticle that come out of the vacuum and return to it. So you need a theory allowing for pairs of particle-antiparticle.