Tyshchenko A. Multiphoton effective interactions in a dense fermionic medium

Тhe effective electromagnetic interaction in dense fermionic environment in two and three spatial dimensions is investigated by means of quantum field theory. In the two-dimensional quantum electrodynamics in medium the polarization operator and the three-photon vertex are calculated and their properties are studied for static case. The effective Lagrangian of the static electromagnetic field of arbitrary configuration in dense medium is constructed. The corresponding nonlinear Maxwell equations in medium are derived and solved for certain cases of static interaction. In three spatial dimensions the three-photon vertex is calculated for arbitrary relations between frequencies and momenta. Detailed description of photon splitting in dense medium has been done.