Yang–Mills theory is a gauge theory based on the SU(N) group, or more generally any compact, semi-simple Lie group. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-Abelian Lie groups and is at the core of the unification of the electromagnetic and weak forces (i.e. U(1) × SU(2)) as well as quantum chromodynamics, the theory of the strong force (based on SU(3)). Thus it forms the basis of our understanding of the Standard Model of particle physics.

Quotes

• The Yang-Mills theories that are the foundation of the Standard Model in modern physics and geometry, are founded in a tradition that has explicitly mixed Maxwellian electricity and mathematics, tensors and topology, charges and fields, poles and holes, functions and spaces: Riemann (1851, 1857) and Gustav Roch (1865), Maxwell (1873), Felix Klein (1890), Hermann Weyl (1913), and W. V. D. Hodge (1940).
  • Martin H. Krieger (15 January 2015). Doing Mathematics: Convention, Subject, Calculation, Analogy. World Scientific. p. 420. ISBN 978-981-4571-86-9. 

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