Electrodynamic absorber theory: a mathematical study.
Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
This work deals with questions that arise in classical and quantum electrodynamics when describing the phenomena of radiation reaction and pair creation. The two guiding ideas are the absorber idea of Wheeler and Feynman (i.e. all emitted radiation will be again be absorbed by matter) and the electron sea idea of Dirac.
In the first part classical dynamics are studied which allow for a description of radiation reaction without the need of renormalization. The starting point are the coupled Maxwell and Lorentz equations without self-interaction. Based on the notion of absorber medium, it is shown how the so-called Lorentz-Dirac equation for radiation reaction emerges and the intimate connection to the famous Wheeler-Feynman action at a distance electrodynamics is explained. Based on this, the mathematical problem of the existence of solutions to the Wheeler-Feynman theory, which is given by a functional differential equation, is rigorously analyzed.
In the second part the phenomenon of pair creation is discussed from a thermodynamic perspective in which the Dirac sea satisfies the absorber condition. Taking Dirac's original idea seriously, the vacuum is to be regarded as an equilibrium state in which all net-electron-electron interactions vanish. Small departures of this equilibrium can be effectively described by introducing pair creation. For the mathematical discussion these seas are considered to consist of infinitely many electrons (in the thermodynamical limit). The mathematical implementation of the quantum mechanical time-evolution for such infinitely many electron seas subject to prescribed external four-vector fields is then carried out in detail. The main result is that the probability amplitudes induced by this time-evolution are well-defined and unique.
In a last part we give a perspective on the quantization of Wheeler-Feynman-like inter- action. Based on the proposed equations, a derivation of the Dirac-Barut equation is given, which seems to predict QED corrections in accordance with the experiment.