Spin and orbital angular momentum in gauge theories: nucleon spin structure and multipole radiation revisited.

We address and solve the long-standing gauge-invariance problem of the nucleon spin structure. Explicitly gauge-invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an impossible task and opens a more promising avenue towards the understanding of the nucleon spin. Our research also justifies the traditional use of the canonical, gauge-dependent angular momentum operators of photons and electrons in the multipole-radiation analysis and labeling of atomic states and sheds much light on the related energy-momentum problem in gauge theories, especially in connection with the nucleon momentum.