A major controversy has arisen in QCD as to how to split the total angular
momentum of the nucleon into separate quark and gluon contributions, and as
to whether the gluon angular momentum can itself be split, in a gauge-invariant
way, into a spin and orbital part. Recall that textbooks on QED tell you that
you cannot split the angular momentum of a photon into a spin part and an
orbital part in a gauge-invariant way, so you would expect the same to be true
for gluons. Yet we claim to be able to measure the spin of the gluons in a
nucleon. Several authors have proposed various answers to these questions and
offered a variety of different expressions for the relevant operators. I survey
some of the ideas put forward and try to assess their physical implications.
