Radiation reaction and classical models of the electron
Date
1988
Authors
Vollick, Daniel Nelson
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Abstract
In this thesis the classical theories concerning the structure and self interaction of the electron are examined. The infamous 1 problem in the transformation of the electromagnetic field momentum is discussed and elucidated in chapter two. The Lorentz-Dirac equation and its non relativistic limit, the Abraham-Lorentz equation, are examined in chapters three and four. Phenomena such as runaway solutions and preacceleration are shown to be related to an unexpected form of internal energy which is known as the Schott energy. It is then shown that this Schott energy is part of the bound electromagnetic energy. Both mass renormalization and the renormalization of the energy momentum tensor are discussed in chapter four. Other possible equations of motion for point particles are looked at in chapter five. In this chapter the exact equation of motion for an extended charge distribution is examined and it is found that for a spherical shell of charge both preacceleration and runaway solutions are absent if the radius of the shell is greater than its classical radius. It is also found that if the radius of the shell is smaller than this radius preacceleration and runaway solutions are present. In chapter six, general relativistic electron models are discussed. The remainder of the thesis deals with classical models which are based on modifications of either Maxwell's or Einstein's theory.