Gauge Theory

Gauge theory is the mathematical framework underlying all fundamental forces in the Standard Model. Its central object is a principal fiber bundle over spacetime with a Lie group as structure group; the gauge field is a connection on that bundle, and the physical field strength is its curvature. Electromagnetism is a U(1) gauge theory, the weak force is SU(2), and the strong force is SU(3). The Yang–Mills equations generalize Maxwell's equations to non-abelian gauge groups, and their quantum mass gap (whether pure SU(2) Yang–Mills on R⁴ has a positive lowest energy excitation) remains one of the Clay Millennium Prize Problems.