Advances in Natural Sciences: Nanoscience and Nanotechnology 8
, 035018 (2017)
Functional integral method in quantum field theory of Dirac fermions in graphene
Nguyen Duc Duoc Phan, Nhu Dat Nguyen, Van Hau Tran, Toan Thang Nguyen and Van Hieu Nguyen
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.