- #1

MathematicalPhysicist

Gold Member

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Here's the link:

http://marcofrasca.wordpress.com/?s=mass+gap

Or he hasn't proven his theorem, math-wise.

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- Thread starter MathematicalPhysicist
- Start date

- #1

MathematicalPhysicist

Gold Member

- 4,699

- 369

Here's the link:

http://marcofrasca.wordpress.com/?s=mass+gap

Or he hasn't proven his theorem, math-wise.

- #2

weburbia

- 28

- 0

- #3

sbrothy

- 212

- 96

http://www.math.columbia.edu/~woit/wordpress/?p=1657

I think the discussion started at the wiki entry.

If his work is correct maybe he can finally edit that article. :)

- #4

Lester

- 33

- 0

The question went this way. I have got a paper published on Physics Letters B

http://arxiv.org/abs/0709.2042" [Broken]

where I stated some theorems producing as a final result the infrared gluon propagator. This propagator displays a spectrum of excitations with a massive ground state. This result relies on a theorem that I claimed to have been proved that maps a massless quartic scalar theory on a Yang-Mills theory. I stated that these theories have common classical solutions that can be used to obtain a quantum field theory describing an identical behavior for both. QFT for the scalar theory was published, authored by me, in Physical Review D

http://arxiv.org/abs/hep-th/0511068" [Broken]

The proof of the mapping theorem was declared wrong by Terry Tao, the Fields medalist, with an intervention on the discussion in the Wiki entry of Yang-Mills theory (see http://en.wikipedia.org/wiki/Talk:Yang–Mills_theory" [Broken] in the section "Removed "Integrable solutions of classical Yang-Mills equations and QFT"). After this criticism I have written to Terry asking for clarifications. Indeed, he removed the corresponding entries in his site Dispersive Wiki claiming the proof was incorrect. He asked to me to get a correct proof to be published in an archival journal. I obtained this last year in Modern Physics Letters A

http://arxiv.org/abs/0903.2357" [Broken]

Terry recognized, in a private communication and removing the entry to my paper in http://tosio.math.toronto.edu/wiki/index.php/Talk:Yang-Mills_equations" (just click on FraE2007 in Terry's removal comment and see also follow-up), that my new proof was indeed correct but that these common solutions between the scalar field theory and the Yang-Mills theory hold, in the more general case, only perturbatively in the strong coupling limit: Mapping exists perturbatively. But note that this is all I need to get my proof completed!

Meantime, a proof on the lattice that the mapping theorem holds also in d=2+1 was obtained by Rafael Frigori and published on Nuclear Physics B

http://arxiv.org/abs/0912.2871" [Broken]

see also

http://marcofrasca.wordpress.com/2009/12/16/mapping-is-confirmed-by-lattice-computations/" [Broken].

So now, the proof is both correct and complete thanks also to the pivotal intervention of Terry Tao that helped me to fix it by pointing out a flaw in the original demonstration. But until Terry will not ask to me to restate the original material, improved as I said, I will not do that.

Currently, I am working out QCD phenomenology using this low-energy limit of Yang-Mills theory that makes all computations manageable. Indeed, low-energy QCD is reduced to a Yukawa model, reducible yet to a Nambu-Jona-Lasinio model with all parameters properly fixed by QCD (see arxiv for this). But this is another story.

About the low fuss that my work produced I do not know. But, since now, it was a great privilege to work these problems out, getting the results published on such important journals and rising the interest of a great mathematician like Terry is.

http://arxiv.org/abs/0709.2042" [Broken]

where I stated some theorems producing as a final result the infrared gluon propagator. This propagator displays a spectrum of excitations with a massive ground state. This result relies on a theorem that I claimed to have been proved that maps a massless quartic scalar theory on a Yang-Mills theory. I stated that these theories have common classical solutions that can be used to obtain a quantum field theory describing an identical behavior for both. QFT for the scalar theory was published, authored by me, in Physical Review D

http://arxiv.org/abs/hep-th/0511068" [Broken]

The proof of the mapping theorem was declared wrong by Terry Tao, the Fields medalist, with an intervention on the discussion in the Wiki entry of Yang-Mills theory (see http://en.wikipedia.org/wiki/Talk:Yang–Mills_theory" [Broken] in the section "Removed "Integrable solutions of classical Yang-Mills equations and QFT"). After this criticism I have written to Terry asking for clarifications. Indeed, he removed the corresponding entries in his site Dispersive Wiki claiming the proof was incorrect. He asked to me to get a correct proof to be published in an archival journal. I obtained this last year in Modern Physics Letters A

http://arxiv.org/abs/0903.2357" [Broken]

Terry recognized, in a private communication and removing the entry to my paper in http://tosio.math.toronto.edu/wiki/index.php/Talk:Yang-Mills_equations" (just click on FraE2007 in Terry's removal comment and see also follow-up), that my new proof was indeed correct but that these common solutions between the scalar field theory and the Yang-Mills theory hold, in the more general case, only perturbatively in the strong coupling limit: Mapping exists perturbatively. But note that this is all I need to get my proof completed!

Meantime, a proof on the lattice that the mapping theorem holds also in d=2+1 was obtained by Rafael Frigori and published on Nuclear Physics B

http://arxiv.org/abs/0912.2871" [Broken]

see also

http://marcofrasca.wordpress.com/2009/12/16/mapping-is-confirmed-by-lattice-computations/" [Broken].

So now, the proof is both correct and complete thanks also to the pivotal intervention of Terry Tao that helped me to fix it by pointing out a flaw in the original demonstration. But until Terry will not ask to me to restate the original material, improved as I said, I will not do that.

Currently, I am working out QCD phenomenology using this low-energy limit of Yang-Mills theory that makes all computations manageable. Indeed, low-energy QCD is reduced to a Yukawa model, reducible yet to a Nambu-Jona-Lasinio model with all parameters properly fixed by QCD (see arxiv for this). But this is another story.

About the low fuss that my work produced I do not know. But, since now, it was a great privilege to work these problems out, getting the results published on such important journals and rising the interest of a great mathematician like Terry is.

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