Momentum map for the Maxwell-Lorentz equations with spinning particle

Abstract

We develop the theory of momentum map for the Maxwell-Lorentz equations with spinning extended charged particle. This theory is indispensable for the study of long-time behaviour and radiation of the solitons of this system. The development relies on the Hamilton-Poisson structure of the system. As an example, we apply the theory to the rotation group of symmetry, calculating the expression for the conserved angular momentum. We check the coincidence of this expression with known classical invariant.