non-abelian gauge groups

Non-abelian gauge groups are mathematical frameworks used in physics to describe forces where the order of interactions matters. Unlike abelian groups (like electromagnetism), where operations commute (e.g., leaving a door open then closed is the same as closed then open), non-abelian groups have elements whose order affects the outcome. This property underpins theories like the strong and weak nuclear forces, where particles interact in complex, non-commutative ways. These groups help scientists understand how fundamental particles behave under these forces, highlighting the rich, intricate symmetry structures that govern subatomic interactions beyond simple, additive effects.