Color confinement in quantum chromodynamics

Prove confinement in quantum chromodynamics by rigorously deriving from the QCD Lagrangian that colored states such as quarks and gluons do not appear as isolated asymptotic states, thereby establishing confinement from first principles.

Background

While phenomenology and lattice simulations support quark and gluon confinement, a rigorous derivation of confinement from the QCD dynamics in four dimensions is still lacking. The author notes that even today there is no real understanding of confinement at a rigorous level.

Confinement is widely regarded as a central open problem in non-abelian gauge theories and is closely related to the Millennium Prize Problem on Yang–Mills theory and the mass gap.