Relativistic Fields with Point Defects

这个项目分为经典和量子物理部分。 经典部分是关于严格分析的经典极限的一个新的动力学理论的相对论性电磁场的拓扑点缺陷，代表点电子。 该理论结合了非线性Maxwell-Born-Infeld场方程和新的点缺陷的Hamilton-Jacobi型运动定律。 这里最重要的问题是特殊的相对论辐射反应问题，现在可以在没有任何先验正则化或重整化的情况下进行研究。 首席研究员还将发展这一理论的广义相对论扩展，这有望在时空和引力场的所谓裸奇点的运动问题上取得进展。 这个理论已经部分地量子化了;现在这个项目的量子部分是关于量子化的完成。 特别地，实现自旋和光子的物理上重要的量子效应是主要目标。 到目前为止，这个理论没有任何困扰主流电磁理论（QED）的臭名昭著的发散问题，预计最终的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，化学和凝聚态物理到电子和电气工程的一切。 正统理论当然取得了巨大的成功，但它也受到了无穷大的困扰，这些无穷大阻碍了在一些问题上的进一步发展。 在这个项目中的研究涉及到一个新的形式主义，旨在克服正统的电磁理论的问题，它已经克服了其中的一些。 由于新的数学定义良好的形式主义正在发展中，更好的定量，严格的，电磁现象的计算模拟可能会被期望。 例如，该理论的经典版本涵盖了高温等离子体的物理学，并应用于空间和实验室（热核聚变）现象。 新量子理论的一个有希望的应用是正电子素物理学，特别是在正电子发射断层扫描中可能有医学应用。

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.