## Yang-Mills mass gap scenario: Further confirmations

Alexander (Sasha) Migdal was a former professor at Princeton University. But since 1996, he is acting as a CEO of a small company. You can read his story from that link. Instead, Marco Bochicchio was a former colleague student of mine at University of Rome “La Sapienza”. He was a couple of years ahead of me. Now, he is a researcher at Istituto Nazionale di Fisica Nucleare, the same of OPERA and a lot of other striking contributions to physics. With Marco we shared a course on statistical mechanics held by Francesco Guerra at the department of mathematics of our university. Today, Marco posted a paper of him on arXiv (see here). I am following these works by Marco with a lot of interest because they contain results that I am convinced are correct, in the sense that are describing the right scenario for Yang-Mills theory. Marco, in this latter work, is referring to preceding publications from Sasha Migdal about the same matter that go back till ’70s! You can find a recollection of these ideas in a recent paper by Sasha (see here). So, what are these authors saying? Using somewhat different approaches than mine (that you can find well depicted here), they all agree that a Yang-Mills theory has a propagator going like

$G(p)=\sum_{n=0}^\infty\frac{Z_n}{p^2-m_n^2+i\epsilon}$

being $Z_n$ some numbers and $m_n$ is given by the zeros of some Bessel functions. This last result seems quite different from mine that I get explicitly $m_n=(n+1/2)m_0$ but this is not so because, in the asymptotic regime, $J_k(x)\propto \cos(x-k\pi/2-\pi/4)/\sqrt{x}$ and zeros for the cosine go like $(n+1/2)\pi$ and then, my spectrum is easily recovered in the right limit. The right limit is properly identified by Sasha Migdal from Padè approximants for the propagator that start from the deep Euclidean region $\Lambda\rightarrow\infty$, being $\Lambda$ an arbitrary energy scale entering into the spectrum. So, the agreement between the scenario proposed by these authors and mine is practically perfect, notwithstanding different mathematical approaches are used.

The beauty of these conclusions is that such a scenario for a Yang-Mills theory is completely unexpected but it is what is needed to grant confinement. So, the conclusion about the questions of mass gap and confinement is approaching. As usual, we hope that the community will face these matters as soon as possible making them an important part of our fundamental knowledge.

Marco Bochicchio (2011). Glueballs propagators in large-N YM arXiv arXiv: 1111.6073v1

Alexander Migdal (2011). Meromorphization of Large N QFT arXiv arXiv: 1109.1623v2

Marco Frasca (2010). Mapping theorem and Green functions in Yang-Mills theory PoS FacesQCD:039,2010 arXiv: 1011.3643v3

### 6 Responses to Yang-Mills mass gap scenario: Further confirmations

1. ohwilleke says:

“I am following these works by Marco with a lot of interest because they contain results that I am convinced are correct, in the sense that are describing the right scenario for Yang-Mills theory.”

Oh, come clean. We know you just support him because his name is Marco too.

• mfrasca says:

Yeah, we just founded a Marcos’ party.

If you solve the same problem (equations), no wonder you get similar results.

• mfrasca says:

Of course, you are correct but here we do not know these solutions a priori and so, obtaining them with different techniques is a strong support to their correctness.

Marco

3. Please take a look at what I have just posted here, regardiung Mass Gap and obtaining exact Yang-Mills propagators: http://jayryablon.wordpress.com/2012/05/24/baryons-and-confinement-exact-quantum-yang-mills-propagators-mass-gap/

• mfrasca says:

Dear Jay,

as you know, claiming a revolution can only be achieved if your results are published on a peer-reviewed journal. This is a step that all we have done and keep on doing. So, my suggestion is not to expect answers through this blog or sites like yours. Put your notes in a good shape and send them to a proper journal.

Cheers,

Marco