Covariant Theory of Electromagnetism and Radiation in Vacuum and Media

Abstract

I study radiation emission by classical relativistic charged particles interacting with strong electromagnetic fields including the case of motion in vacuum (Larmor radiation) as well as in matter (Cherenkov radiation). I employ a consistent covariant formulation throughout the thesis. I provide detailed description of the covariant constitutive relations and constitutive tensor which relates the electromagnetic fields to the displacement fields. I then construct Lorentz-invariant generalizations of the electric permittivity, magnetic permeability, and index of refraction, explicitly discussing the case of an isotropic medium. I describe and characterize radiation reaction in classical electromagnetism using the Lorentz-Abraham-Dirac (LAD) and Landau-Lifshitz (LL) particle equations of motion. I contrast these approaches with the Eliezer-Ford-O'Connell (EFO) equation, which improves on some of the shortcomings of both the LAD and LL equations. I also show that the EFO equation has a novel feature; the invariant acceleration magnitude of a particle can be limited in certain field configurations. This motivates a search for a more general context which would contain a universal upper limit to acceleration as a general principle. I compare the limiting acceleration of the EFO equation of motion to the limiting field strength theory of electromagnetism, the Born-Infeld (BI) theory. I show that BI theory places an upper limit on the invariant electric-like eigenvalue of the electromagnetic field tensor. I discuss the formulation of BI theory, and nonlinear electromagnetic theories in general, in terms of the constitutive tensor introduced in the context of matter. I then calculate the invariant dielectric constants corresponding to a nonlinear theory. I discuss the effects of the limiting field properties of BI theory using the example of relativistic heavy ion collisions. The emission of Cherenkov radiation by a particle moving faster than the local speed of light within a medium is another radiation phenomenon I explore as it has not yet been addressed in a manner consistent with the relativistic formulation of Larmor radiation. Cherenkov radiation does not require acceleration. Using the covariant formulation, I contrast the Cherenkov with the Larmor radiation process in vacuum which does requires acceleration. I use the formulation of covariant constitutive relations to derive a covariant form of the Cherenkov radiation reaction force on a uniformly moving charged particle in an isotropic medium. I then discuss how our formalism can be generalized to allow for acceleration of the particle and derive a unified Larmor-Cherenkov radiation reaction force.