Webrelaunch 2020

AG Mathematische Physik (Summer Semester 2018)

Seminar: Tuesday 9:45-11:15 SR 2.66

Vu Hoang (University of Texas at San Antonio)

On self-force in higher-order electrodynamics

In this talk, I discuss the unsolved problem of obtaining equations of motion for relativistic charged particles. The problem has a long history going back to work of Lorentz and Abraham, who modeled charged particles as rigid spheres. Motivated by applications in quantum theory, Dirac abandoned the rigid sphere model and proposed a model for point-like charged particles. By applying conservation of energy and momentum, he obtained the Lorentz-Dirac equation of motion, which gives rise to unphysical runaway solutions. One obvious problem with Dirac's calculation can be traced to the fact that the field energy of a point particle is infinite. A possible way out was suggested by B. Podolsky, F. Bopp and others: one can modify Maxwell's equations by adding a term containing higher-order derivatives of the field tensor to the Lagrangian. Unfortunately, Lorentz forces corresponding to the self-fields of particles are still not defined in a straightforward way. In a recent breakthrough however, M. Kiessling and A. S. Tahvildar-Zadeh prove the local well-posedness of the initial-value problem of point charges and field in Bopp-Podolsky electrodynamics. In the main part of the talk, I will discuss the recent successful rigorous computation of the self-force in Bopp-Podolsky electrodynamics by M. Radosz and myself as well as its connections to work by Gratus, Perlick and Tucker.