Abstract

We investigate the inner structure of a general SU(2) (naturally including SO(3)) symmetry system—the fermion-gauge field interaction system, and achieve naturally a set of gauge invariant spin and orbital angular momentum operators of fermion and gauge fields by Noether theorem in general field theory. Some new relations concerning non-Abelian field strengths are discovered, e.g., the covariant transverse condition, covariant parallel condition ( i.e., non-Abelian divergence, non-Abelian curl ) and simplified SU(2) Coulomb theorem. And we show that the condition that Chen et al obtained to construct their gauge invariant angular momentum operators is a result of some fundamental equations in the general field theory. The results obtained in this paper present a new perspective to look at the overall structure of the gauge field, and provide a new viewpoint to the final resolution of the nucleon spin crisis in the general field theory. Specially, the achieved theory in this paper can calculate the strong interactions with isospin symmetry and solves the serious problem without gauge invariant angular momenta in strong interaction systems with isospin symmetry, and then the achieved predictions in the calculations can be exactly measured by particle physics experiments due to their gauge invariant properties.

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.92.056003