Yang–Mills Mass Gap

Millennium Prize Problem: prove that quantum Yang–Mills theory on R⁴ exists and has a strictly positive mass gap Δ > 0.

Specifications & Metrics

type

Open Problem

Core Principles & Analysis

• One of the seven Millennium Prize Problems, announced in 2000 with a 1,000,000-dollar prize, and still unsolved.
• The official statement: prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R⁴ and has a mass gap Δ > 0.
• Experiment and computer simulations suggest the mass gap exists in the quantum Yang–Mills theories underlying the strong interaction, but no rigorous proof is known.

Sources

• Wikipedia: Yang–Mills existence and mass gap