To develop a systematic treatment of the self-interaction problem in classical gauge theories and general relativity, we study tenable manifestations of self-interaction: topological phases, and rearrangements of degrees of freedom appearing in the action. We outline the occurrence of topological phases in pure field systems. We show that the rearranged Maxwell-Lorentz electrodynamics is a mathematically consistent and physically satisfactory theory which describes new entities, dressed charged particles and radiation. We extend this analysis to cover different modifications of the Maxwell-Lorentz electrodynamics and the SU(N) Yang-Mills-Wong theory. We take a brief look at a subtle mechanism of self-interaction in classical strings. Turning to general relativity, we note that the total energy and momentum of a system with nontrivial topological content, such as a black hole, are ambiguous, coordinatization-dependent quantities, which resembles the situation with paradoxical decompositions in the Banach-Tarski theorem.

中文翻译：

---

经典规范理论和引力中的自相互作用

为了对经典规范理论和广义相对论中的自相互作用问题进行系统的处理，我们研究了自相互作用的站得住脚的表现形式：拓扑相和出现在动作中的自由度的重新排列。我们概述了纯场系统中拓扑相的发生。我们表明，重新排列的麦克斯韦-洛伦兹电动力学是一种数学上一致且物理上令人满意的理论，它描述了新实体、带电粒子和辐射。我们扩展此分析以涵盖 Maxwell-Lorentz 电动力学和 SU(N) Yang-Mills-Wong 理论的不同修改。我们简要地看一下古典弦乐中一种微妙的自相互作用机制。转向广义相对论，