Relativistic Fields with Point Defects

本项目分为经典物理部分和量子物理部分。经典部分是对具有点电子拓扑缺陷的相对论电磁场动力学新理论的经典极限的严格分析。该理论结合了非线性麦克斯韦-玻恩-因菲尔德场方程和新颖的点缺陷Hamilton-Jacobi型运动定律。这里最重要的问题是狭义相对论辐射反应问题，现在不需要任何先验的正则化或重整化就可以研究它。首席研究员还将发展这一理论的广义相对论延伸，这有望在所谓的时空和引力场的裸奇点运动问题上取得进展。这个理论已经部分被量子化了；项目的量子部分现在涉及到量子化的完成。特别是，实现物理上重要的自旋和光子量子效应是主要目标。到目前为止，该理论没有任何困扰流行电磁理论（QED）的臭名昭著的散度问题，预计最终理论也将完全表现良好。电磁学是基础物理理论中应用最广泛的部分。它涉及从原子物理、化学、凝聚态物理到电子和电气工程的所有领域。正统理论当然取得了巨大的成功，但它也受到了无穷无尽的困扰，这些无穷无尽的问题阻碍了它在许多问题上的进一步发展。本项目的研究涉及一种新的形式主义，它旨在克服正统电磁理论的问题，并且已经克服了其中的一些问题。由于正在发展的新的数学上定义良好的形式体系，可以期望对电磁现象进行更好的定量、严格的计算模拟。该理论的经典版本涵盖了，例如，高温等离子体的物理学，应用于空间和实验室（热核聚变）现象。新量子理论在正电子物理方面的应用前景广阔，特别是在正电子发射断层扫描方面的医学应用。

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.