Yang-Mills Existence and Mass Gap: The Yang-Mills Existence and Mass Gap problem arises from quantum field theory, the framework underlying the Standard Model of particle physics. Yang-Mills theory describes elementary particles via non-abelian gauge fields (e.g., gluons in quantum chromodynamics). The "mass gap" refers to the observed phenomenon that the lightest particle in such theories has a positive mass, despite the equations suggesting massless waves. The challenge is to rigorously construct a quantum Yang-Mills theory in four-dimensional spacetime and prove it has a mass gap. This requires merging quantum mechanics with special relativity in a mathematically consistent way—a feat not yet achieved. Lattice gauge theory offers numerical insights, but analytical proof is lacking. Solving this Clay Millennium Prize problem would bridge physics and mathematics, validating the theoretical foundation of modern particle physics.
Add Comment + Vote ( 1 )...
There are currently no comments !