In this paper, we study the dynamics of a charged particle interacting with the non-null electromagnetic knot wave background. We analyze the classical system in the Hamilton–Jacobi formalism and find the action, the linear momentum and the trajectory of the particle. Also, we calculate the effective mass and the emitted radiation along the knot wave. Next, we quantize the system in the classical strong knot wave background by using the strong-field QED canonical formalism. We explicitly construct the Furry picture and calculate the Volkov solutions of the Dirac equation. As an application, we discuss the one-photon Compton effect where we determine the general form of the S-matrix. Also, we discuss in detail the first partial amplitudes in the transition matrix in two simple backgrounds and show that there is a pair of states for which these amplitudes are identical.

中文翻译：

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强非零结波背景下带电粒子的非线性动力学

在本文中，我们研究了带电粒子与非零电磁结波背景相互作用的动力学。我们分析了 Hamilton-Jacobi 形式主义中的经典系统，并找到了粒子的作用、线性动量和轨迹。此外，我们计算有效质量和沿结波发射的辐射。接下来，我们使用强场 QED 规范形式对经典强结波背景下的系统进行量化。我们明确地构建了 Furry 图片并计算了 Dirac 方程的 Volkov 解。作为一个应用程序，我们讨论了单光子康普顿效应，我们确定了 S 矩阵的一般形式。还，