Angular momentum and light-front scattering theory

The role of the Leutwyler and Stern spin operator in the angular momentum analysis of light-front scattering theory is analyzed. The equations of formal scattering theory are transformed to the $\xi$ picture using the unitary operator $C\left(\xi \right)$ recently developed by the author. This operator depends on the two angles which determine the direction of the three-vector part of a lightlike four-vector $\xi$. It is shown that an invariant version of light-front perturbation theory developed earlier by the author is related to the standard theory by the unitary operator $C\left(\xi \right)$. It is also shown how to carry out a partial-wave analysis of the Lippmann-Schwinger-like equations obtained by summing a subset of the diagrams of this invariant form of light-front perturbation theory. The analysis presented here makes clear that the $\xi$ picture overcomes many of the difficulties due to the interaction dependence of light-front angular momentum operators, in particular the difficulties arising from the fact that the individual diagrams of light-front pertubation theory are not rotationally invariant.