Mathematical PhysicsUnsolved
Yang–Mills Existence and Mass Gap
Prove that quantum Yang–Mills theory exists and has a positive mass gap.
Overview
This problem asks for a rigorous mathematical construction of quantum Yang–Mills theory in four dimensions and a proof that it exhibits a mass gap.
Why It Matters
Yang–Mills theory underpins the Standard Model. A rigorous construction would bridge physics intuition with mathematical foundations.
Current Status
Physicists have strong evidence, but a fully rigorous mathematical construction in 4D remains uncompleted.
What a Solution Would Require
A mathematically rigorous definition meeting axioms plus proof of a positive mass gap.