  We present a study of the tensorial structure of the hadronic matrix elements
of the angular momentum operators $\bm{J}$. Well known results in the
literature are shown to be incorrect, and we have taken pains to derive the
correct expressions in three different ways, two involving explicit physical
wave packets and the third, totally independent, based upon the rotational
properties of the state vectors. Surprisingly it turns out that the results are
very sensitive to the type of relativistic spin state used to describe the
motion of the particle i.e. whether a canonical (i.e. boost) state or a
helicity state is utilized. We present results for the matrix elements of the
angular momentum operators, valid in an arbitrary Lorentz frame, both for
helicity states and canonical states.
  These results are relevant for the construction of angular momentum sum
rules, relating the angular momentum of a nucleon to the spin and orbital
angular momentum of its constituents. It turns out that it is necessary to
distinguish carefully whether the motion of the partons is characterized via
canonical or helicity spin states. Fortunately, for the simple parton model
interpretation, when the proton moves along $OZ$, our results for the sum rule
based upon the matrix elements of $J_z$ agree with the often used sum rule
found in the literature. But for the components $J_x, J_y$ the results are
different and lead to a new and very intuitive sum rule for transverse
polarization.
