Dynin claims to have proven Witten's statement

In fact, his paper has no summary about his conclusion. Instead, Schiller, in his book, claims that YM only exists for SU(2) and SU(3), if I understand correctly.Prove that for any compact simple global gauge group, a nontrivial quantum Yang-Mills theory exists on Minkowski time-space and has a positive mass gap.

I guess that the million dollar will still remain at the Clay Institute for a while.

Since it is a nonlinear field theory, Yang-Mills has an extremely rich and non-trivial dynamical structure. Treating Yang Mills from the perspective of perturbative quantum field theory is likely to grossly underestimate its full spectrum of implications. This is one of the reasons why electroweak symmetry breaking has so many puzzles associated with it and why QCD is a theoretical mess. I made this point in almost all the papers I published...

ReplyDeleteIn my opinion, getting to appreciate the dynamic structure of Yang Mills theory and its natural tendency to approach bifurcations and chaos leads to intriguing solutions for the many puzzles of the Standard model (the mass and flavor hierarchy problems, the emergence of gauge interactions, the breaking of P and CP symmetries, the fine tuning problem and so on).

Ervin,

ReplyDeletechaos and bifurcations in YM theory? That might be right. But these look like mathematical games to me. Is there any evidence for this? All researchers think that the present situation "grossly underestimates the full spectrum of implications."

As you know, I disagree. For me, this is exactly what string theorists and many other theorists always say: there is so much yet to be discovered. The reality? No unexpected discovery since decades. (And many expected ones, such as supersymmetry, gone.)

There is no experimental evidence that the standard model or general relativity are wrong...

The point I was trying to make is that, although there is no explicit evidence for chaos and bifurcations in the SM, there are signatures of this behavior that may explain some of its many unresolved puzzles. For example, the presence of non-trivial attractors in the Renormalization Group flow is a subject of growing interest. Chaos and bifurcations may start to have an impact as energies are ramped up beyond SM. Besides, Quantum Chaos is NOT a mathematical game, it has been confirmed in many experimental settings and there is a lot of literature on this topic.

DeleteThe subject matter is simply too involved to start discussing it here. Here are some links, in case you are interested:

http://www.worldscientific.com/worldscibooks/10.1142/2584

http://iopscience.iop.org/0295-5075/82/1/11001

http://www.worldscientific.com/doi/abs/10.1142/S0218127408020756

http://prespacetime.com/index.php/pst/article/view/348

http://www.ejtp.com/articles/ejtpv7i23p75.pdf

http://www.worldacademicunion.com/journal/1749-3889-3897IJNS/IJNSVol3No3Paper02.pdf

I also wish to reply on your comment that: "There is no experimental evidence that the standard model or general relativity are wrong..."

ReplyDeleteAs of today, there are two proven deviations from the predictions of the Standard Model: 1) neutrino masses and mixings, 2) the magnetic moments of muon and tau-lepton.

There is no evidence for deviations from General Relativity with one possible exception: DIRECT evidence for gravitational waves (we only have indirect evidence for it from binary pulsars).

Ervin, I am a more conservative woman:

ReplyDeleteNonzero neutrino masses are easily built into the standard model.

The magnetic moment values are not sure to be deviations. (See the presentation slides by the experts.)

Lack of gravity wave detection does not disprove GR.

Clara,

DeleteI tend to be conservative too but I have an opposite view on these issues. Specifically,

1) Nonzero neutrino masses can be incorporated in EXTENSIONS of the Standard Model. But they are clearly not part of the Standard Model, as it is presented in textbooks.

2) Unlike the electron magnetic moment, the measured magnetic moments of muon and tau deviate from the predicted g = 2 value and it is presently unclear where these deviations come from. The anomaly has not gotten away despite years of computations and analysis. Even worse, refutation of low-scale SUSY makes the anomaly more serious than previously anticipated.

3) Gravitational waves are a direct outcome of General Relativity whose equations show that weak gravitational fields propagate in vacuum with the speed of light.

One can argue that these are deficiencies but not refutations of the theory. It is a question of semantics, but they clearly hint (along with other considerations) that both SM and GR are only effective field theories that cannot be stretched beyond their limits.

Let's agree to disagree.

Indeed, we disagree :-)

ReplyDelete