Magnetic scattering: pairwise little group and pairwise helicity [Special Theoretical Physics Colloquium as part of the DP Roy Memorial Lecture]

I discuss how to construct the S-matrix for the scattering of electrically and magnetically charged particles. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. I will discuss the general construction of such states. The resulting "pairwise helicity" is identified with the quantized "cross product" of charges e1 g2- e2 g1 for  every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S-matrix elements, as well as the full partial wave decomposition for the 2 -> 2 fermion-monopole S-matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves.  We show a potential resolution of Callan's long-standing semiton problem in our approach. Finally we show how these pairwise states can be understood dynamically as dressed states which incorporate the effects of soft photons, and provide a novel fully field theoretic derivation of Dirac quantization in terms of a geometric Berry phase.