Ukrainian mathematical congress - 2009
Alexander Glushkov (Odessa State University OSEU, Odessa, UkraineÓ)
QED Energy Operator Approach and QED Lines Moments Technique in Relativistic Quantum Theory
We present the foundations of a new, formally exact quantum electro dynamical (QED) operator perturbation formalism and quantum electro dynamical spectral lines moments technique in relativistic theory of quantum systems. A new, highly exact, ab initio approach to description of the relativistic atomic systems includes a correct account of relativistic, correlation, nuclear, radiative effects within a gauge-invariant QED operator perturbation theory. The correlation corrections of high orders are accounted within the Green functions method. New QED moments technique and QED energy approach allow to find the radiation lines moments of different orders and calculate it within Gell-Mann and Low adiabatic S-matrix formalism . New approach gives an effective and simple (simultaneously correct) description of such phenomena as DC, AC strong and super strong field Stark and Zeemane effects, multi-photon phenomena in atomic and firstly nuclear systems in super intensive laser field, new cooperative laser (raser, gaser)-beta, gamma-nuclear effects in atomic and molecular systems, electron-positron pair production (EPPP) in heavy nuclei collisions etc. In the last case a new numerical approach is developed to define the cross-section of the nucleus-nucleus collision with EPPP by means of the modified expression through imaginary part of the complex energy within S-matrix Gell-Mann and Low formalism. Besides, we present a new, advanced procedure of quantization of the quasi-stationary (scattering) and stationary for relativistic quantum systems. An adaptation of the mapped Fourier grid method for the relativistic Dirac equation is applied to the collision problem. Modelling nuclear ensembles in a super strong laser field provides opening a new field of nuclear quantum optics.