Relativistic Fields with Point Defects

这个项目分为经典物理部分和量子物理部分。经典部分严格分析了具有拓扑点缺陷表示点电子的相对论电磁场新动力学理论的经典极限。该理论将点缺陷的非线性Maxwell-Born-Infeld场方程组与一种新的Hamilton-Jacobi型运动定律相结合。这里最重要的问题是特殊的相对论辐射反应问题，它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。首席研究人员还将开发这一理论的广义相对论扩展，它有望在所谓的时空和引力场的裸奇点的运动问题上取得进展。这个理论已经部分被量子化了；该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的量子效应是主要目标。到目前为止，该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。电磁学是物理学基本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方方面面。正统理论当然取得了巨大的成功，但它也受到了无限的困扰，这些无限阻碍了在许多问题上取得进一步进展。这个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。由于正在开发的新的数学上定义明确的形式主义，对电磁现象的更好的定量、严格的计算模拟可能是可望的。例如，该理论的经典版本涵盖了高温等离子体的物理学，并将其应用于空间和实验室(热核聚变)现象。新量子理论的一个很有前途的应用是正电子物理学，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.