Relativistic Charge Dynamics in Electromagnetic Fields
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In this thesis we consider the motion of a charged particle in strong electromagnetic background elds, having in mind applications to state-of-the-art high-power lasers. To nd solutions of the Lorentz force equation of motion, we make use of Noether's theorem to identify conserved quantities of the charge dynamics. We will explain how, given enough symmetries, a dynamical system becomes integrable or, with a maximum number of conserved quantities, maximally superintegrable. Beginning with charged particles in vector background elds, we shall show that the relevant symmetry group is the Poincar e group. The dynamics for constant and univariate elds is classi ed, and their integrability properties are clari ed. We then move on to the problem of a particle in a scalar background eld and show that the symmetry group is extended to the conformal group. We then present examples of elds which include Poincar e, dilation and special conformal symmetries leading to varying extents of integrability.