Yang–Mills existence and mass gap

In mathematical physics, the Yang–Mills existence and mass gap problem is an unsolved problem and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 to the one who solves it. The problem is phrased as follows: In this statement, a 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.