Yang–Mills equations
Partial differential equations whose solutions are instantons / From Wikipedia, the free encyclopedia
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This article discusses the Yang–Mills equations from a mathematical perspective. For the physics perspective, see Yang–Mills theory
In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also found significant use in mathematics.
Solutions of the equations are called Yang–Mills connections or instantons. The moduli space of instantons was used by Simon Donaldson to prove Donaldson's theorem.