The kinetic description of vacuum particle creation in the oscillator representation

The oscillator representation is used for the non-perturbative description of vacuum particle creation in a strong time-dependent electric field in the framework of scalar QED. It is shown that the method can be more effective for the derivation of the quantum kinetic equation (KE) in comparison with the Bogoliubov method of time-dependent canonical transformations. This KE is used for the investigation of vacuum creation in periodical linear and circular polarized electric fields and also in the case of the presence of a constant magnetic field, including the back reaction problem. In particular, these examples are applied for a model illustration of some features of vacuum creation of electron-positron plasma within the planned experiments on the X-ray free electron lasers.