Orbital Angular Momentum: How to Define it and How to Measure it

Abstract

Abstract. In the context of the controversy concerning the ambiguities in the definition of quark and gluon angular momentum we explain pedagogically the origin of these ambiguities and stress that there are fundamentally only three physically relevant variants. We give precise expressions for the sum rules involving them. We consider their measurement, both experimentally and on the lattice, and discuss some attempts to calculate them in models.

Topological approach to proton spin problem: decomposition controversy and beyond

“…In one of the earliest critique [18] of [7] Leader argues that canonical momentum and canonical angular momentum are the correct ones, and also presents a lucid discussion on some salient features of quantum electrodynamics (QED) and QCD. In a recent contribution [10] he explains the difference between kinetic and canonical versions. For the sake of clarity and completeness certain points have to be added on this issue.…”

“…A simple calculation shows that the combined two terms in (10) S λµν +M λµν lead to the standard experession of the total angular momentum making use of ∇.E = 0, whereas the total expression for J αµν directly gives this expression…”

“…In the light of new insights gained in the preceding section it becomes somewhat easier to address this question. We begin with the QED example as presented in [7]: their equations ( 6) to (10). A unique decomposition of the vector potential…”

“…Setting aside the controversy, the current status of the proton spin problem reviewed in the literature [2,[8][9][10][11]45] indicates that the standard sum rules and the decomposition of the angular momentum operators for calculating physical observables employing perturbative QCD have not succeeded in solving the problem. Could there be a crucial role of nonperturbative QCD in the proton spin problem?…”

“…The main question is whether the gauge invariant separation of spin and orbital angular momenta of quarks and gluons respecting relativistic invariance was indeed possible contrary to the textbook wisdom. Intense debate followed, and now seems to have been settled [10][11][12] with the consensus that manifest Lorentz covariance and gauge invariance cannot be satisfied simultaneously, see the earlier comment [13], there are only two distinct angular momenta -kinetic and canonical, and experimental conditions determine as to what is physically meaningful. One of the important fall outs of this debate is the reappraisal of conceptual issues and their pedagogical elucidation.…”