Electrodynamics of Non-topological Solitons

In this thesis, we study a class of non-topological solitons known as "Q-balls" which arise in complex scalar field theories with U(1) symmetry. We focus on the case where the U(1) symmetry is gauged and the theory admits a coupling to electromagnetism; the corresponding solitons are known as "gauged Q-balls". Using numerical simulations, we examine the dynamical behaviour of these objects in various scenarios. First, we investigate the classical stability of gauged Q-balls under assumptions of axial symmetry. Considering two different forms for the scalar field potential, we find evidence for gauged Q-ball configurations which remain stable with respect to axisymmetric perturbations of the fields. We also find evidence for unstable configurations which are quickly destroyed in response to the perturbations (for example, through dispersal of the fields or via fragmentation into smaller structures). Next, we investigate head-on collisions of gauged Q-balls at relativistic velocities. We test the effects of the electromagnetic coupling strength, initial velocity, relative phase, and relative charge of the colliding binary on the outcome of the collision. Depending on the values of these parameters, we observe a variety of distinct phenomena such as gauged Q-ball mergers, fragmentation, charge transfer, charge annihilation, Q-ring formation, and electromagnetic radiation production. Finally, we investigate the dynamics of gauged Q-balls using fully three-dimensional numerical simulations. Extending the previous analyses, we find evidence for configurations which remain classically stable against generic perturbations in three spatial dimensions. We also consider off-axis collisions of gauged Q-balls and find that the impact parameter can play a significant role in determining the outcome of the collision. Together, these results address several key questions about the dynamics of non-topological solitons in general and the stability of gauged Q-balls in particular.