Nonlinear dynamics of a charged particle in a strong non-null knot wave background
arXiv:2006.13972 · doi:10.1142/S0217751X20501134
Abstract
In this paper, we study the dynamics of the charged particle interacting with the non-null electromagnetic knot wave background. We analyse 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 -matrix. Also, we discuss in details 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.
Minor typos corrected, references added. 40 pages, LaTeX file
References in corpus (9)
- Non-Linear Compton Scattering of Ultrashort and Ultraintense Laser Pulses
- Nonlinear double Compton scattering in the full quantum regime
- Knotted solutions, from electromagnetism to fluid dynamics
- Exact classical and quantum dynamics in background electromagnetic fields
- New knotted solutions of Maxwell's equations
- Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics
- Motion of charged particles in an electromagnetic knot
- On the existence of the field line solutions of the Einstein-Maxwell equations
- Hopfion solutions in gravity and a null fluid/gravity conjecture