Chaos and quantum field theory


Dmitry is still on is point trying to prove me wrong (see his post here). Of course, I have a theory mathematically sound and he has nothing and so the discussion is somewhat uneven from the start. He is saying that my point

In order to build a meaningful quantum field theory, the initial conditions should be properly chosen.

is wrong. This means that we can start to develop a meaningful QED without electrons or photons and obtain identical results. A fact that is blatantly wrong. QED spectrum is done with plane waves representing the spectrum of the theory. Without this choice you are at odds with experiments. This is a crucial point for quantum field theory and applies wherever you need to compute a cross section or a decay rate. Choosing different solutions at the start (e.g. by changing initial conditions) will produce a different quantum field theory and this can be at odds with experiments. This is a well-known fact and an example is given through the computations generally done e.g. for the Casimir effect.

So, he continues

“I believe, it is actually wrong. Let us again take a hamiltonian classical system with self-interaction. To get the intermittency (i.e., periodic orbits becoming chaotic trajectories and vise versa), it is enough to fix initial conditions and than vary the coupling constant, as I have explained … Since one has running coupling in a QFT without sweating, one will have intermittency as well in the Schwinger-Dyson equations for Keldysh Green functions. So, strictly speaking, one can only get rid of chaos at the RG fixed point which corresponds to CFT anyway (that is — no particles, nor quasiparticles, just unparticles ;-)).”

I would agree with such an argument if intermittency could be a useful solution to build a quantum field theory and would give us a spectrum to start with. E.g. I would like to see how is the glueball spectrum, to be observed into experiments with a lot of people currently eager to detect it, with a chaotic classical solution like this. You are in serious troubles as you do not even have a Fourier expansion. So, no Fourier expansion no spectrum. Indeed, Dmitry has no such result but just a prejudice: Chaotic classical solutions must be important for Yang-Mills theory. This without a proof that, he claims, should rely on me. But I have already shown that the theory is consistent and complete with integrable solutions and this was my aim. He is just claiming the contrary without providing a serious support to his prejudice.

After this rather questionable facts by his side and having him admitted that I am right as

Currently, there is no formulation of a quantum field theory starting with classical chaotic solutions.

he exposes his “would be”s about such a matter.

Let me comment about this discussion and how all this should be interpreted. Whenever you are smart enough to produce a theory and get it published you will get opinions from two different kind of people.  You will find interested people and criticizing people and this is in the matter of things. Criticizing people could be very useful wherever is able to support arguments with serious evidence. But most of times they will just criticize you on the ground of prejudices they have and these prejudices are those you have just demolished with your theory. So, to move an idea from the status of a prejudice to a status of a theory a strong mathematical and experimental support is needed.  A typical historical example has been the question of aether supporting the propagation of electromagnetic waves. A lot of people kept on believing on that till their death even after a strong evidence for relativity was achieved. This behavior belongs to our community, it was never lost, and we have to cope with it anytime we produce something new. It could imply delay into the acceptance of a theory but it is just human behavior and cannot be changed.

Let me repeat again. My approach is well developed and provides a glueball spectrum (to be observed experimentally), propagators and running coupling making the formulation of a Yang-Mills theory in the infrared complete. Propagators and running coupling are in very good agreement with lattice computations that come out in this somewhat unexpected direction. The same can be said with the spectrum but assuming that the lowest glueball is at about 500 GeV and has been already seen as \sigma resonance or f0(600). The same interpretation should apply to f0(980). This is in agreement with analysis done with dispersion relations by Narison, Mennessier, Ochs (see here) and Minkowski (see here).

What does one have on the side of classical chaotic solutions and quantum field theory? Substantially nothing as also admitted by Dmitry. No theory, no predictions, nothing. So, it can only be classified as a prejudice and a prejudice generally turns out to be wrong. My aim starts and ends when I have showed that my theory is mathematically sound and consistent and I get predictions that could be confirmed or not.  I do not have the burden to prove that, as one of my hypothesis does not like to someone, I have also to formulate my theory without it.

As a conclusion, I would greatly appreciate a formulation of a quantum field theory starting with chaotic solutions that applies to a realistic model of reality. I do not believe in betting but it would be tempting to put a wager on this.

%d bloggers like this: