Abelian and Non-Abelian Gauge Theory

Gauge theories describe how fundamental forces work, using mathematical frameworks called groups. Abelian gauge theories involve groups where the order of operations doesn't matter—changing the sequence yields the same result (like adding numbers). An example is electromagnetism. Non-Abelian gauge theories involve groups where order matters, meaning the sequence affects the outcome—common in the strong and weak nuclear forces. These differences shape the behavior of particles and forces, influencing how interactions occur at the subatomic level. In essence, Abelian theories are simpler, while Non-Abelian theories capture more complex, interdependent interactions in nature.