Q-LUMPS AND THEIR INTERACTIONS

The nonlinear O(3) sigma-model in (2 + 1) dimensions, modified by the addition of a potential term. admits solutions of Q-ball type. Such configurations, given the name Q-lumps, carry an integer-valued topological charge in addition to the conserved Noether charge. For a special choice of potential, they may be constructed explicitly in terms of simple functions via a natural extension of the usual Bogomolny equations. The existence of a Bogomolny bound guarantees that Q-lumps minimize the energy for any given value of Q. Their stability is discussed in detail and their interactions are investigated for low impact velocities using an adiabatic approximation. Forces transverse to the direction of motion lead to many possibilities, including circular orbits. Even head-on collisions have exotic scattering angles.