Existence of Travelling Wave Solutions to the Maxwell-Pauli and   Maxwell-Schr\"odinger Systems
  We study two mathematical descriptions of a charged particle interacting with it's self-generated electromagnetic field. The first model is the one-body Maxwell-Schr\"odinger system where the interaction of the spin with the magnetic field is neglected and the second model is the related one-body Maxwell-Pauli system where the spin-field interaction is included. We prove that there exist travelling wave solutions to both of these systems provided that the speed $|v|$ of the wave is not too large. Moreover, we observe that the energies of these solutions behave like $\frac{mv^2}{2}$ for small velocities of the particle, which may be interpreted as saying that the effective mass of the particle is the same as it's bare mass. 
Kim Petersen and Jan Philip Solovej
math-ph math.MP