A special structure of the scattering operator and infrared divergences in quantum electrodynamics
Lev Sakhnovich
备注：
This paper is closely connected with our paper arXiv:1602.07087 and developes further some important results from arXiv:1602.07087. In the current version, we add some results on a special structure of the scattering operators and use these results in order to justify our approach to divergence problems
We assume that the unperturbed operators $A_0$ are known. Then, the fact that the scattering operators $S$ and the unperturbed operators $A_0$ are pairwise permutable provides some important information about the structure of the scattering operators. Using this information and the ideas from the theory of generalized wave operators, we present a new approach to the divergence problems in quantum electrodynamics. We show that the so called infrared divergences appeared because the deviations of the initial and final waves from the free waves were not taken into account.
Quantum parity conservation in planar quantum electrodynamics
在微扰理论中，对无质量宇称偶$U(1)\times U(1)$平面量子电动力学（QED $_3$）模型，证明了各阶的量子宇称守恒.两个无质量费米子的存在需要在Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein（BPHZL）重整化方法的框架中的Lowenstein-Zimmermann（LZ）减法方案，以减去由紫外减法在1-和2-环处引起的红外发散，然而由于模型的超重整化，紫外发散被限制到2-环。最后，证明了BPHZL重整化方法对所考虑的模型保持宇称性，而对普通的无质量宇称-偶$U(1)$ QED $_3$则相反.
