  The commissioning of the high power laser facility Extreme Light
Infrastructure - Nuclear Physics (ELI-NP) at Bucharest-Magurele (Romania)
allows the in-depth study of nonlinear interactions in Strong Field Quantum
Electrodynamics (SF-QED). The present paper analyzes the SF-QED processes
possible to study at ELI-NP. Carrying out such experiments will allow finding
answers to many fundamental QED questions. After a brief review of the first
experiment (E-144 SLAC) which confirmed the existence of nonlinear QED
interactions of high-energy electrons with photons of a laser beam, we
presented the fundamental QED processes that can be studied at ELI-NP in the
multi-photon regime along with the characteristic parameters of the laser beam
used in the QED interaction with electrons.
  To prepare an experiment at ELI-NP, it is necessary to analyze both the
kinematics and the dynamics of the interactions. Therefore, we first reviewed
the kinematics of linear QED processes and then the corresponding Feynman
diagrams. For nonlinear, non-perturbative multi-photon QED interactions, the
Feynman diagram technique must be adapted from linear to nonlinear processes.
This is done by switching to quantum fields described by Dirac-Volkov dressed
states, of particles in an intense electromagnetic (EM) field. This allows the
evaluation of the amplitude of the physical processes and finally the
determination of the cross-sections of these processes.
  SF-QED processes of multi-photon interactions with strong laser fields can be
investigated taking into account the characteristics of the ELI-NP facility in
the context of QED vacuum pair production of electron-positron pairs and
energetic gamma rays.
  Finally, we present some similar experimental projects from other research
centers, in different stages of implementation.
