Path Integral and Electromagnetic Field

Horst-Heino von Borzeskowski, Michael B. Mensky

Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков

We study the dynamics of multi-level quantum systems under the influence of electromagnetic field.Basing on the path integral approach to the quantum density matrix and transitions probability we represent functional averaging electromagnetic field influence.We demonstrate that the transition probability can be written as a path integral of real functional (the product of exponent and cosine).The numerical integration algorithm of the transitions probability in energy representation was developed.The numerical simulations of the quantum system dynamics under electromagnetic field action describe the well-known Rabi oscillations, their fluctuations and multi-photon quantum transitions.

Luiz C. L. Botelho

Mark S. Swanson

Alexander S. Lukyanenko, Inna Lukyanenko

A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase space. This regularization allows one to obtain a representation of the path integral over trajectories in the configuration space. This form of the path integral is useful for the formulation of perturbation theory in an external electromagnetic field.