Evidence item

The official Clay problem description defines the Yang–Mills challenge as proving existence of a non-trivial four-dimensional quantum theory for any compact simple gauge group together with a positive mass gap. DIRECT_TEXT

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Source: Quantum Yang–Mills Theory · locator {} · excerpt hash sha256:1e90e915d67fc7c694dcda270e44e72a0e20eaf0b754bda4f8f767494b2cbba0

Yang–Mills Existence and Mass Gap. 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. ... A quantum field theory has a mass gap Δ if H has no spectrum in the interval (0, Δ) for some Δ > 0.