tailieunhanh - Báo cáo "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- (QED3 ) 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 | VNU Journal of Science Mathematics - Physics 23 2007 22-27 Eliminating on the divergences of the photon self - energy diagram in 2 1 dimensional quantum electrodynamics Nguyen Suan Han1 Nguyen Nhu Xuan2 1 Department of Physics College of Science VNU 334 Nguyen Trai Hanoi Vietnam 2 Department of Physics Le Qui Don Technical University Received 15 May 2007 Abstract The divergence of the photon self-energy diagram in spinor quantum electrodynamics in 2 1 dimensional space time- QEDf 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. 1. Introduction It is well known that the gauge theories in 2 1 dimensional space time though super-renormalizable theory 1 showing up inconsistence already at one loop arising from the regularization procedures adopted to evaluate ultraviolet divergent amplitudes such as the photon self-energy in QED3. In the latter if we use dimensional regularization 2 the photon is induced a topological mass in contrast with the result obtained through the Pauli-Villars scheme 3 where the photon remains massless when we let the auxiliary mass go to infinity. Other side this problem is important for constructing quantum field theory with low dimensional modern. This report is devoted to show up the inconsistencies not arising in QED3 if the gauge invariance of theory is considered carefully step by step in those calculations by above methods of regularization for the photon self-energy diagram. The paper is organized as follows. In the second section the photon self-energy is calculated by the dimensional regularization. In the third section this problem is done by the Pauli-Villars method. Finally we draw our conclusions. 2. Dimensional regularization In this section we calculate the photon self-energy diagram in QED3 given by Fig. 1 Corresponding author. Tel 84-4-069515341 .