Non-Abelian gauge theory is a framework within quantum field theory where gauge transformations map spacetime to elements of compact simple Lie groups (specifically SU(N)), characterized by matrix-valued generators and structure constants that define the commutation relations of the associated Lie algebra. The core mechanism involves constructing covariant derivatives using representation-specific matrices in non-homogeneous transformation laws, ensuring local symmetry for fields transforming under various representations while introducing self-interacting gauge bosons distinct from Abelian theories. This concept extends the Standard Model's microscopic understanding by generalizing U(1) symmetries to groups with multiple degrees of freedom and internal group-space rotations governed by infinitesimal Lie algebra parameters.
Non-Abelian gauge theory is a framework within quantum field theory where gauge transformations map spacetime to elements of compact simple Lie groups (specifically SU(N)), characterized by matrix-va…