About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD.

1, Why do we need to solve QCD exactly?
Of course, solving any field theory exactly is a dream. But what I mean is why do we feel more urgent to solve exactly QCD than other theories such as $\phi^4$ theory? Is the reason that perturbation can not be used in QCD in some cases such as the confinement problem?

2, Why do we need the large N expansion?
People say that QCD is a zero-parameter theory because the coupling constant $g$ is changing with the RG flow. And to do a first approximation, we should introduce a parameter to expand in. The parameter turns out to be the $N$ in $SU(N)$. But similar arguments can be given for $\phi^4$ theory where the coupling $\lambda$ is also a RG flow dependent quantity. Then why do we naturally and comfortably expand in $\lambda$ there? And even after we introduce the large N expansion, we still do the analysis with the help of feynman diagrams which means that we already use the perturbation theory. So does it mean that the argument 'large N limit is introduced because QCD is a zero-parameter theory' incorrect and actually it is introduced simply for simplifying the calculations?

I really appreciate if someone can discuss these issus here.

The second question has been answered here. And I think the answer to the first question is exactly what I guessed in this post, partly also because QCD is very important.


closed as too broad by David Z Apr 21 '16 at 7:17

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Hi Wein - could you edit your post to make it clear what one question you're asking that these are the two steps of? Right now I think the connection is not so clear. $\endgroup$ – David Z Apr 21 '16 at 7:18
  • $\begingroup$ Ok, if you think they are not related with each other clearly, I can divide this post into two ones. But I just think that that will weaken the motivation for these questions and make discussions somewhat repeated in two posts. $\endgroup$ – Wein Eld Apr 21 '16 at 7:54
  • $\begingroup$ Who says solving QCD exactly is a priority? In fact, who is even trying to do that? $\endgroup$ – Mitchell Porter Apr 21 '16 at 7:55
  • $\begingroup$ @MitchellPorter Solving QCD exactly is one the seven Clay Institutes's Millennium Problems. $\endgroup$ – Wein Eld Apr 21 '16 at 8:10
  • $\begingroup$ @Wein Eld - I thought the problem is to prove that the theory is mathematically well-defined and that it exhibits confinement. $\endgroup$ – Mitchell Porter Apr 21 '16 at 10:37