Existence of Travelling Wave Solutions to the MaxwellPauli and MaxwellSchrödinger Systems
Abstract
We study two mathematical descriptions of a charged particle interacting with it's selfgenerated electromagnetic field. The first model is the onebody MaxwellSchrödinger system where the interaction of the spin with the magnetic field is neglected and the second model is the related onebody MaxwellPauli system where the spinfield 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.3936
 Bibcode:
 2014arXiv1402.3936P
 Keywords:

 Mathematical Physics;
 35Q51;
 35Q40;
 35Q61