Nonperturbative calculation of QED processes involving 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 use of analytical solutions of particle dynamical equations, 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 interest in QED processes in a strong field composed of two counterpropagating laser waves, but the exact solution 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 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 solution is demonstrated and its validity is proven clearly. The result has the advantages of Lorentz covariance, clear structure, and close similarity to the solution in a plane-wave field, and thus favors convenient application.

• Received 12 September 2015

DOI:https://doi.org/10.1103/PhysRevA.92.062105