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The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution.
The problem is phrased as follows:
In this statement, a quantum Yang–Mills theory is a non-abelian quantum field theory similar to that underlying the Standard Model of particle physics; R 4 {\displaystyle \mathbb {R} ^{4}} is Euclidean 4-space; the mass gap Δ is the mass of the least massive particle predicted by the theory.
Therefore, the winner must prove that:
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