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Yang–Mills existence and mass gap
Construct four-dimensional quantum Yang–Mills theory for every compact simple gauge group and prove that it has a positive mass gap.
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| 1 | +{ | |
| 2 | + "domain": "physics-astronomy", | |
| 3 | + "topics": [ | |
| 4 | + "mathematical-physics" | |
| 5 | + ], | |
| 6 | + "type": "proof", | |
| 7 | + "source": { | |
| 8 | + "key": "clay", | |
| 9 | + "name": "Clay Millennium Prize Problems", | |
| 10 | + "url": "https://www.claymath.org/millennium/yang-mills-the-maths-gap/", | |
| 11 | + "curator": "Clay Mathematics Institute", | |
| 12 | + "poser": "Clay Mathematics Institute, with the problem description by Arthur Jaffe and Edward Witten", | |
| 13 | + "status": "unsolved", | |
| 14 | + "as_of": "2026-10-20", | |
| 15 | + "prize": "$1,000,000", | |
| 16 | + "catalog": "0521c19bbd38" | |
| 17 | + } | |
| 18 | +} | |