Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
Pure four-dimensional confining quantum Yang–Mills theory is expected to have a positive energy gap above its vacuum. Constructing the continuum theory rigorously and proving the gap remains an open Clay Millennium problem. This must not be conflated with exact chiral-limit QCD, whose spontaneously broken chiral symmetry gives massless Nambu–Goldstone modes.
Physical QCD with nonzero light-quark masses has a gapped hadron spectrum. In the exact massless-light-quark limit, however, spontaneous chiral-symmetry breaking produces massless pions, so the full theory does not have a positive spectral gap. The Clay problem concerns pure Yang–Mills theory.
A satisfactory solution must construct a nontrivial four-dimensional quantum Yang–Mills theory with appropriate axiomatic properties and prove a strictly positive mass gap.
wp-physics-yang_mills_mass_gapnlab-physics-yang_mills_mass_gapclay-yang-mills-mass-gaptong-gaugeEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Pure confining four-dimensional quantum Yang–Mills theory is expected to have a positive spectral gap above the vacuum; rigorous continuum construction and proof remain open.
The target is a collective, organizational, or scale-dependent phenomenon of the source constituents and interactions; it is not a mere list or classical sum of constituents.
clay-yang-mills-mass-gaptong-gaugewp-physics-yang_mills_mass_gapEach relation below starts at this concept.
No direct relations are authored in this direction.