Basics of quantum field theory of electromagnetic interaction processes in single-layer grapheme

Abstract

The content of this work is the study of electromagnetic interaction in single-layer graphene by means of the perturbation theory. The interaction of electromagnetic field with Dirac fermions in single-layer graphene has a peculiarity: Dirac fermions in graphene interact not only with the electromagnetic wave propagating within the graphene sheet, but also with electromagnetic field propagating from a location outside the graphene sheet and illuminating this sheet. The interaction Hamiltonian of the system comprising electromagnetic field and Dirac fermions fields contains the limits at graphene plane of electromagnetic field vector and scalar potentials which can be shortly called boundary electromagnetic field. The study of S-matrix requires knowing the limits at graphene plane of 2-point Green functions of electromagnetic field which also can be shortly called boundary 2-point Green functions of electromagnetic field. As the first example of the application of perturbation theory, the second order terms in the perturbative expansions of boundary 2-point Green functions of electromagnetic field as well as of 2-point Green functions of Dirac fermion fields are explicitly derived. Further extension of the application of perturbation theory is also discussed.