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Mathematical Physics
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Yang–Mills Existence and Mass Gap
Establish a rigorous quantum Yang–Mills theory on R⁴ and prove that it has a positive mass gap — the lowest excitation sits strictly above the vacuum.
- Impact
- 91 /100
- Funded
- $7,400
- Donors
- 134
- Of goal
- 25%
Why this matters
Yang–Mills theory is the mathematical skeleton of the Standard Model. A mass gap explains why the strong force is short-range and why glueballs should exist — yet a fully rigorous construction remains open.
What a solution unlocks
- A non-perturbative foundation for QCD-like theories
- New constructive quantum field theory techniques
- Predicted glueball spectra on firm mathematical ground
Downstream impact
Closing the mass gap would crown decades of constructive QFT and give particle physics a theorem where it currently has extraordinarily successful — but still formal — calculations.
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