This project is divided into a classical and a quantum physical part. The classical part is concerned with the rigorous analysis of the classical limit of a new dynamical theory of relativistic electromagnetic fields with topological point defects that represent point electrons. This theory combines the nonlinear Maxwell-Born-Infeld field equations with a novel Hamilton-Jacobi type law of motion for the point defects. The most important issue here is the special relativistic radiation reaction problem, which can now be investigated without any a priori regularization or renormalization. The principal investigator will also develop a general relativistic extension of this theory, which promises progress on the problem of motion of so-called naked singularities of space-time and the gravitational field. The theory has already been partly quantized; the quantum part of the project now is concerned with the completion of the quantization. In particular, the implementation of the physically important quantum effects of spin and photon are the primary goals. So far the theory is free of any of the notorious divergence problems that plague the prevailing electromagnetic theory (QED), and it is expected that the final theory will also be entirely well-behaved.
Electromagnetism is the most widely applicable part of fundamental physical theory. It touches everything from atomic physics, chemistry, and condensed matter physics to electronics and electrical engineering. The orthodox theory has certainly been hugely successful, yet it has also been plagued by infinities that have stood in the way of further progress on a number of issues. The research in this project involves a new formalism which is designed to overcome the problems of the orthodox electromagnetic theory and which has already overcome some of these. As a result of the new mathematically well-defined formalism under development, better quantitative, rigorous, computational simulation of electromagnetic phenomena may be expected. The classical version of the theory covers, for instance, the physics of high temperature plasma, with applications to space and laboratory (thermonuclear fusion) phenomena. A promising application of the new quantum theory is to positronium physics, which in particular may have medical applications in positron emission tomography.
