The conceptual origins of Maxwell’s equations and gauge theory

 

Chen Ning Yang

 

Already in Faraday’s electrotonic state and Maxwell’s vector potential, gauge freedom was an unavoidable presence. Converting that presence to the symmetry principle that underpins our successful standard model is a story worth telling.

 

 

It is often said that after Charles Augustin de Coulomb, Carl Friedrich Gauss, AndréMarie Ampère, and Michael Faraday discovered the four experimental lawsconcerning electricity and magnetism, James Clerk Maxwell added the displacement current and thereby created the great set of Maxwell’s equations.That view is not entirely wrong, but it obscures the subtle interplay betweensophisticated geometrical and physical intuitions that led not only to thereplacement of “action at a distance” by field theory in the 19th century butalso, in the 20th century, to the very successful standard model of particle physics.