Functional integral method in quantum field theory of Dirac fermions in graphene

Abstract

The purpose of this work is to elaborate the functional integral method in quantum field theory of Dirac fermions in the Dirac fermion gas of a graphene single layer at vanishing absolute temperature. The starting point to be assumed as the fundamental principle of the theory is the explicit expression of the action functional of this system. The efficient mathematical tool to be used in the study is the generating functional containing the Grassmann parameters anticommuting with the Dirac fermion field operators. The analytical expression of the generating functional of free Dirac fermion system is exactly derived and efficiently used in the study of 2n-point Green functions of free Dirac fermions. Then the celebrated Hubbard-Stratonovich transformation is applied to rewrite the functional integral of the interacting system of Dirac fermions in a new form expressing in terms of a scalar Hermitian quantum field describing the collective excitations in the interacting Dirac fermion gas and related to the graphene plasmons.