Analytical solution for Klein-Gordon equation and action function of the solution for Dirac equation in counter-propagating laser waves

Abstract

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.

8

References in corpus (7)

• Prolific pair production with high-power lasers
• Pair production in counter-propagating laser beams
• On the Schwinger limit attainability with extreme power lasers
• Analytical tools for investigating strong-field QED processes in tightly focused laser fields
• A Novel Solution to the Klein-Gordon Equation in the Presence of a Strong Rotating Electric Field
• Few-Photon Electron-Positron Pair Creation by Relativistic Muon Impact on Intense Laser Beams
• Furry picture transition rates in the intense fields at a lepton collider interaction point

Cited by in corpus (9)

• Advances in QED with intense background fields
• Classical and quantum particle dynamics in univariate background fields
• Classical and quantum dynamics of a charged scalar particle in a background of two counterpropagating plane waves
• Non-Linear Compton Scattering in a Strong Rotating Electric Field
• Multi-channel Interference in Nonperturbative Multiphoton Pair Production by Gamma Rays Colliding
• Ultrarelativistic electrons in counterpropagating laser beams
• Seed and vacuum pair production in strong laser field
• Ground state and the spin precession of the Dirac electron in counterpropagating plane electromagnetic waves
• Localized solutions of the Dirac equation in free space and electromagnetic space-time crystals