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In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We represent the equations of the movement for the fermionic field and expression for energy of an electron taking into account influence of a vacuum of the electromagnetic field.

Functional Approach for the Description of Vacuum Influence on Electron States