Yang–Mills theory

A gauge field theory in which interactions arise from fields associated with continuous symmetry groups. It underlies the modern descriptions of the strong and weak nuclear forces.

Gauge symmetry: A redundancy in field descriptions that leaves observable physical quantities unchanged. Local gauge symmetry constrains the fields and interactions in Yang–Mills theory.
Lie group: A group that is also a smooth manifold, allowing its symmetries to vary continuously. Yang–Mills gauge symmetries are built from continuous groups.
Classical electromagnetism: The classical theory of electric and magnetic fields and their sources. Its Abelian gauge structure supplied the model that Yang and Mills sought to generalize.
Quantum chromodynamics: The quantum field theory of quarks and gluons, describing the strong interaction. It is the SU(3) Yang–Mills gauge theory at the core of the strong interaction.
Yang–Mills existence and mass gap: The unsolved problem of proving that four-dimensional quantum Yang–Mills theory exists and has a positive mass gap. This mathematical challenge concerns the rigorous foundations of quantum Yang–Mills theory.
Gauge field: A field whose components mediate interactions and transform under local symmetry operations. Yang–Mills theory makes gauge fields dynamical carriers of force.
Lie algebra: The vector space of infinitesimal generators associated with a Lie group, equipped with a bracket operation. Its generators determine the gauge-field components and their interaction structure.
Chen-Ning Yang: A Chinese-American theoretical physicist whose work helped establish non-Abelian gauge theory. Yang co-developed the theory with Robert Mills in 1954.
Electroweak interaction: The unified gauge description of electromagnetic and weak interactions. Its SU(2) gauge sector is a Yang–Mills theory combined with a U(1) sector.
Mass gap: A positive minimum energy separating the vacuum from the first excited state of a quantum field theory. Quantum Yang–Mills theory is expected to exhibit a mass gap despite massless classical gauge fields.

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