Consequences of Yang-Mills and Mass Gap?

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SUMMARY

The discussion centers on the consequences of solving the Yang-Mills existence and mass gap problem, a Millennium Prize Problem. Participants agree that while there are no new physical consequences expected, existing phenomena such as asymptotic freedom, color confinement, and chiral symmetry breaking are well understood through numerical calculations. However, a rigorous mathematical definition of quantized non-abelian gauge theories remains elusive, highlighting the need for a formal proof of existence. The implications of this problem extend beyond physics, raising questions about potential applications in other scientific fields.

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  • Understanding of Yang-Mills theory
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What are the consequences of a possible solution to Yang-Mills existence and mass gap problem? Are the consequences only physical or they will also have applications to other branches of science or life? If yes, what are they?
 
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are you referring to the millenium problem http://www.claymath.org/millennium/Yang-Mills_Theory/
 
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Yes, I'm referring to the Millennium Problem.
 
I don't think that there are any new physical consequences. We already see asymptotic freedom, color confinement, chiral symmetry breaking; we are able to calculate hadron masses, form factoprs etc. on the lattice with < 5% deviation theor. - exp.

What's missing is a rigorous mathematical definition (or at least a proof of existence) of quantized non-abelian gauge theories and a rigorous derivation of the results. Confinement is still purely understood, most calculations are done numerically, ...

That's why it's a mathematical millenium problem ;-)
 
Thanks for your opinion tom.stoer. I was thinking the same thing, but I was just curious whether it was going to have applications to other branches of science or it will be purely mathematical.
 

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