That paper contains a mathematical proof of confinement of Yang-Mills theory using the Kugo-Ojima criterion. It come out from a collaboration with Masud Chaichian. It underwent extensive review, well before it was submitted to a journal, by Kugo himself and several other well-known physicists that helped to improve it. Kugo-Ojima criterion has the effect to yield the exact beta function for these theories and the running coupling so obtained is in excellent agreement with what is expected from known results both experimental and theoretical ones. Also, this agrees fairly well with the functional form of the beta function exactly obtained by Shifman et al. for SUSY Yang-Mills theory.

Cheers,

Marco

]]>Connes’ approach has an important application in physics as the author and his collaborators were able to show that the Standard Model of elementary particles can be completely derived in terms of noncommutative geometry. There has been some tension due to the observed mass of the Higgs particle that did not seem to fit the prevision by Connes et al. but so far, as I heard directly from him, this point seems to be fixed. Here would help some expert comments from people well aware of this matter.

I used the Connes’ ideas mostly in the realm of non-relativistic quantum mechanics as you can judge by my paper but the insights they contain are wide-ranging and I hope more success to them. Surely, they represent a sound starting point to approach quantum gravity but most as to be said yet.

Cheers,

Marco

]]>I am not a physicist but interested in the fundamental questions. Most of NCG is beyond my skills but I have tried to understand parts of it. I agree that the work by Connes is unique in that it seems to capture fundamental aspects of the SM. I wonder why this work does not get more attention. Maybe the failure of string theory will make alternative approaches more popular.

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