Since the establishment of quantum field theory on the basis of quantum mechanics and special relativity in 1930s, it has been an effective calculation theory to describe the interaction of microscopic high-energy particles. When quantum field theory is used for theoretical calculation, the most effective calculation method is still the mature and complete perturbation theory step-by-step calculation. However, in perturbation step-by-step calculation, high-order (circular graph) calculation will be difficult to diverge, so renormalization scheme is needed to separate non-physical divergence and maintain physical limit. In this way, the calculation of high-order cycle graphs becomes so complicated and difficult that the renormalization limit can only be obtained by approximate calculation and processing. Because the limited contribution of renormalization (radiation correction) is generally small, it is very important to study physical problems in depth. Therefore, in the in-depth study of many important physical problems and processes, it is especially necessary to consider and seek the at least limited radiation correction contribution of unicyclic graph renormalization. In this paper, the Lorentz invariant coupling model of strong interaction between proton P- antiproton P and neutral meson π0 is adopted, and the analytical calculation method of single-cycle renormalization vertex function λ c (p, q) in the strong coupling model of proton π 0 meson is emphatically studied. In the process of processing, starting from the vertex correction factor from "unicyclic graph" to "tree graph", this paper adopts the scheme of "momentum normalization" and uses the matrix function expansion method to separate the non-physical divergence, thus obtaining the analytical calculation formula λ c (p, q) with limited physics. Furthermore, λ c (p, q) is expressed as elementary algebraic function and transcendental algebraic function by Feynman's three-parameter integral formula, Wick rotation and large momentum integral limit method. Because λ c (p, q) contains transcendental algebraic function (function series) which can't be calculated strictly, this paper introduces the method of "convergence factor", and after reasonable treatment of a small amount of pole drift in the calculation formula, seeks this transcendental algebraic function with good convergence. Then the approximate calculation method of "average equivalence" is introduced to establish a complete and effective new analytical calculation method of λ c (p, q). Finally, based on the established new method, the "elementary algebraic function" and "transcendental algebraic function" in λ c (p, q) are theoretically calculated, and the final analytical calculation result of λ c (p, q) is obtained, and the radiation correction of strong coupling vertex angle is discussed. This calculation result will provide reference for studying the theoretical calculation of higher-order effect of particle reaction in Lorentz invariant coupling model and discussing the effective analytical calculation method of renormalization.

In quantum field theory, it is a basic method to study particle interaction by using quantum field theory perturbation to theoretically calculate various QED reaction processes. This method is not only helpful to analyze and discuss the microscopic mechanism in high energy physics, but also helpful to provide reference for modern accurate measurement technology. However, all the interacting quantum field theories have the difficulty of "ultraviolet divergence" of high-order circular graphs when they are used in perturbation calculation; Various renormalization theories of quantum field theory are introduced to overcome this divergence difficulty. After the transformation, the divergence difficulty is solved. Based on the perturbation theory of quantum field theory, this paper studies the Moller scattering problem of three generations of charged leptons and its renormalization mixed cyclic chain diagram effect by using the unified standard model of electricity and weakness for a class of reactions that have attracted much attention in high energy physics. For this kind of renormalization chain graph propagator to be used in this paper, we should first extend the photon renormalization chain graph propagator with a single lepton ring to the photon renormalization chain graph propagator with three generations of lepton mixed rings, which will involve a series of important problems such as how to find the composition of this kind of photon renormalization chain graph propagator with mixed rings and renormalization calculation. In this paper, the composition of this propagator will be found out reasonably by using the relevant research results in the existing literature, and the renormalization calculation will be completed, so as to obtain the strict calculation results of this renormalization mixed chain graph propagator. Using this result, we also study the Moller scattering of three generations of charged leptons under the propagation of this mixed ring chain diagram, and calculate the differential cross section of the scattering. In addition, the problem of radiation correction is deeply analyzed and important results are given. This paper can not only provide valuable theoretical calculation results for accurately testing the electric and weak unified standard model, but also provide some valuable research results for Moller scattering problems involved in modern accurate measurement applications.

Since the establishment of quantum field theory at the beginning of last century, quantum field theory is a successful phenomenological theory and an effective calculation method to describe the interaction of microscopic high-energy particles. When using quantum field theory for theoretical calculation, the mature and perfect calculation method is still perturbation theory. It is easy to calculate low-order (tree diagram) perturbation with perturbation theory, and there is no difficulty of "divergence" However, it is difficult to "diverge" when calculating high-order (circular) perturbation. Although renormalization theory can reasonably eliminate "divergence", the resulting renormalization calculation problem will lead to extremely complicated and difficult theoretical calculation. The renormalization theoretical calculation of quantum field theory, especially the "exact" theoretical calculation, has been studied for nearly a century, but so far there has been no major breakthrough in the calculation method.