Gauge theories

Gauge theories are at the heart of modern field theory. They are based on the idea of a local gauge symmetry, associated with a Lie group. Quantum electrodynamics (QED), which gives us astounding agreement between theory and experiment, is an Abelian gauge theory associated with the Abelian group U(1). The Standard Model of particle physics, which extends QED to the weak and strong interactions, is also a gauge theory, associated with the non-Abelian group SU(3) × SU(2) × U(1). As we shall see, local gauge invariance requires the existence of spin-one gauge bosons which mediates interactions. The photon is the gauge boson of electrodynamics and mediate the electric force, the W± and Z0 are the gauge bosons which mediate the weak force, and gluons mediate the strong forces. The ideas and techniques of gauge theories have made their way into nuclear and condensed matter physics from particle physics, and have played a large role in modern mathematics.