Abelian Gauge Theory

Abelian gauge theory is a framework in physics that describes how certain fundamental forces, like electromagnetism, operate using mathematical fields. The term "Abelian" refers to a property where the mathematical operations involved commute, meaning the order of interactions doesn't matter. This theory uses the concept of gauge symmetry, which ensures the laws of physics stay consistent even when certain changes are made to the fields. In essence, Abelian gauge theory provides the mathematical foundation for understanding how forces like electromagnetism work by describing the behavior of force-carrying particles (like photons) and their interactions with matter.