Mathematical physics
Millennium Prize Problem
Status: Open
Status last verified
Yang–Mills Existence and Mass Gap
Construct quantum Yang–Mills theory on four-dimensional space-time with mathematical rigour, and prove that its lightest particle has strictly positive mass.
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Suggested experiments
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A small lattice gauge model
Implement a Metropolis simulation of a Z2 or U(1) lattice gauge model on a tiny lattice and measure the average plaquette. Use it to learn the vocabulary, not to test the conjecture.
Establishes: Measurements of a toy model on a finite lattice.
Does not establish: Anything about the existence or mass gap of 4D quantum Yang–Mills theory.