Light-Cone Representation of the Spin and Orbital Angular Momentum of Relativistic Composite Systems
Stanley J. Brodsky, Dae Sung Hwang, Bo-Qiang Ma, Ivan Schmidt
TL;DR
The paper develops a comprehensive light-cone Fock-state framework to represent spin, orbital angular momentum, and form factors of relativistic composite systems. By constructing explicit two-particle light-cone wavefunctions in QED and Yukawa theory, it connects the Schwinger anomalous magnetic moment to constituent spin and orbital motion and provides exact representations for electromagnetic and gravitational matrix elements. A central result is the universal vanishing of the anomalous gravitomagnetic moment B(0) for any composite system, derived from Lorentz boosts in the light-cone formalism. The work also demonstrates how spectral Pauli-Villars integration can model bound states while preserving Lorentz properties, thereby offering a versatile laboratory to test spin-structure propositions in hadrons.
Abstract
The matrix elements of local operators such as the electromagnetic current, the energy momentum tensor, angular momentum, and the moments of structure functions have exact representations in terms of light-cone Fock state wavefunctions of bound states such as hadrons. We illustrate all of these properties by giving explicit light-cone wavefunctions for the two-particle Fock state of the electron in QED, thus connecting the Schwinger anomalous magnetic moment to the spin and orbital momentum carried by its Fock state constituents. We also compute the QED one-loop radiative corrections for the form factors for the graviton coupling to the electron and photon. Although the underlying model is derived from elementary QED perturbative couplings, it in fact can be used to simulate much more general bound state systems by applying spectral integration over the constituent masses while preserving all of the Lorentz properties, giving explicit realization of the spin sum rules and other local matrix elements. The role of orbital angular momentum in understanding the "spin crisis" problem for relativistic systems is clarified. We also prove that the anomalous gravitomagnetic moment B(0) vanishes for any composite system. This property is shown to follow directly from the Lorentz boost properties of the light-cone Fock representation and holds separately for each Fock state component. We show how the QED perturbative structure can be used to model bound state systems while preserving all Lorentz properties. We thus obtain a theoretical laboratory to test the consistency of formulae which have been proposed to probe the spin structure of hadrons.