Construction of a quark spin operator

We discuss how, in null-plane quantized quark models, the total angular momentum operator can be decomposed into approximately conserved, commuting orbital angular momentum and quark spin operators. This decomposition is relevant for the construction of a U(6) ×{} U(6) ×{} O(3) ("constituent quark") classification algebra. Such an algebra has been extensively utilized in phenomenological analyses of matrix elements of the vector and axial-vector currents, but has to date been explicitly constructed only in the free-quark model. Extending this construction to theories of interacting quarks, we identify some features of the free-quark result which are not generally applicable. Specifically, we argue that the U(6) ×{} U(6) ×{} O(3) algebra is only approximately boost invariant, and that quark pairs provide correction terms in the calculation of current matrix elements.