Parallel to the construction of gauge invariant spin and orbital angular momentum for QED in paper (I) of this series [1], we present here an analogous but non-trivial solution for QCD. 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 structure.PACS numbers: 11.15.-q, 13.88.+e, 14.20.Dh,14.70.DjAs a composite particle, the nucleon naturally gets its spin from the spin and orbital motion of its constituents: quarks and gluons. From a theoretical point of view, the first task in studying the nucleon spin structure is to find out the appropriate operators for the spin and orbital angular momentum of the quark and gluon fields. Given these operators, one can then study their matrix elements in a polarized nucleon state, and investigate how these matrix elements can be related to experimental measurements. Pitifully and surprisingly, after 20 years of extensive discussions of the nucleon spin structure [2,3,4,5], this first task was never done, and even largely eluded the attention of the community.At first thought, it seems an elementary exercise to derive the quark and gluon angular momentum operators. From the QCD Lagrangianone can promptly follow Nöther's theorem to write down the conserved QCD angular momentum:

We show that the (j, 0) ⊕ (0, j) representation space associated with massive particles is a concrete realisation of a quantum field theory, envisaged many years ago by Bargmann, Wightman and Wigner, in which bosons and antibosons have opposite relative intrinsic parities. Demonstration of the result requires a careful ab initio study of the (j, 0) ⊕ (0, j) representation space for massive particles, introducing a wave equation with well defined transformation properties under C, P and T, and addressing the issue of nonlocality required of such a theory by the work of Lee and Wick.

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We demonstrate, using two different quark models of hadrons, that there should be isodoublets of dibaryons with strangeness -3 and 7 = 1,2, which are stable with respect to strong decay.

We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular momentum eigenstates. We split, from the total angular momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.Comment: 5 pages, no figure; published in Phys.Rev.D (Rapid Communications