反向传播laser波中Klein-Gordon方程的解析解及Dirac方程解的action函数
Analytical solution for Klein-Gordon equation and action function of the solution for Dirac equation in counter-propagating laser waves
摘要：
对于强电磁场参与的QED过程，特别是当前和未来强激光装置提供的强电磁场参与的QED过程，非微扰计算一般采用Furry图像，并利用粒子动力学方程的解析解，如Klein-Gordon方程和Dirac方程。然而，只有有限的场配置，如平面波场可以解析求解方程。研究表明，在由两个反向传播的激光波组成的强场中的QED过程的显着兴趣，但在这样的字段的精确解是遥不可及的。本文受平面波场中解的结构观察的启发，发展了一种新的方法，得到了Klein-Gordon方程的解析解，并等价地得到了Dirac方程在该场中解的作用函数，在最大动力学参数条件下，存在一个惯性系，在该惯性系中粒子的自由动量远大于其它场的动力学动量参数论证了新解的适用范围，并证明了新解的有效性。所得结果具有洛伦兹协方差、结构清晰、与平面波场解相似等优点，便于应用。
英文摘要：
Nonperturbative calculation of QED processes participated by a strong electromagnetic field, especially provided by strong laser facilities at present and in the near future, generally resorts to the Furry picture with the usage of analytical solutions of the particle dynamical equation, such as the Klein-Gordon equation and Dirac equation. However only for limited field configurations such as a plane-wave field could the equations be solved analytically. Studies have shown significant interests in QED processes in a strong field composed of two counter-propagating laser waves, but the exact solutions in such a field is out of reach. In this paper, inspired by the observation of the structure of the solutions in a plane-wave field, we develop a new method and obtain the analytical solution for the Klein-Gordon equation and equivalently the action function of the solution for the Dirac equation in this field, under a largest dynamical parameter condition that there exists an inertial frame in which the particle free momentum is far larger than the other field dynamical parameters. The applicable range of the new solution is demonstrated and its validity is proven clearly. The result has the advantage of Lorentz covariance, clear structure and close similarity to the solution in a plane-wave field, and thus favors convenient application.
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