Ukrainian mathematical congress  2009
Alexander Glushkov (Odessa State University OSEU, Odessa, Ukraineà) 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 gaugeinvariant 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 GellMann and Low adiabatic Smatrix formalism [1]. 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, multiphoton phenomena in atomic and firstly nuclear systems in super intensive laser field, new cooperative laser (raser, gaser)beta, gammanuclear effects in atomic and molecular systems, electronpositron pair production (EPPP) in heavy nuclei collisions etc. In the last case a new numerical approach is developed to define the crosssection of the nucleusnucleus collision with EPPP by means of the modified expression through imaginary part of the complex energy within Smatrix GellMann and Low formalism. Besides, we present a new, advanced procedure of quantization of the quasistationary (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.
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