Feynman path-integral strong-field dynamics calculation method

The emergence and development of ultrafast intense lasers and attosecond measurement techniques have made it possible to observe and control the motions of electrons on a timescale of attoseconds and a spatial scale of atoms. With the improvement of experimental measurement accuracy, higher requirements are put forward for the accuracy of theoretical calculation methods. Extracting temporal and spatial information about ultrafast dynamics from experimental results through using theoretical models presents a significant challenge. Compared with the exact solutions of the time-dependent Schrodinger equation, the Feynman path-integral method for strong-field dynamics calculations offers a simpler model and higher computational efficiency. The electronic wave packet is regarded as a particle with different initial states, and by analyzing the motion of the particle, the causes of various nonlinear physical phenomena in strong fields can be clarified. This work introduces the saddle point approximation into strong field dynamics calculations based on the strong field approximation theory. Furthermore, the Coulomb-corrected strong field approximation method, trajectory-based Coulomb-corrected strong field approximation method, and Coulomb quantum trajectory strong field approximation method are presented in detail. This review aims to provide relevant methods and literature references for studying strong field dynamics theoretical calculations and also to present some ideas for developing new algorithms.