Yang–Mills existence and mass gap

Millennium Prize Problem

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: Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R 4 {\displaystyle \mathbb {R} ^{4}} and has a mass gap Δ > 0.

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