Eliminating on the Divergences of the Photon Self - Energy Diagram in (2+1) Dimensional Quantum Electrodynamics

The divergence of the photon self - energy diagram in spinor quantum electrodynamics in $(2+1)$ dimensional space time- $(QED_3)$ is studied by the Pauli - Villars regularization and dimensional regularization. Results obtained by two different methods are coincided if the gauge invariant of theory is considered carefully step by step in these calculations.
Comment: 6 pages, 1 figure