A Systematization for One-Loop 4D Feynman Integrals-Different Species of Massive Fields

• 作者: G. Dallabona O. A. Battistel
• 来源期刊: 现代物理(英文)
• 学科: 医学
• 关键词: FEYNMAN INTEGRALS Perturbative AMPLITUDES
• 年，卷（期）: 2012,（10）
• 页码范围: 1408-1449
• 页数: 42页
• 分类号: R73

摘要

A systematization for the manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one loop perturbative solutions of Quantum Field Theory, is proposed. A previous work on the same issue is generalized to treat theories and models having different species of massive fields. An improvement on the strategy is adopted so that no regularization needs to be used. The final results produced, however, can be converted into the ones of reasonable regularizations, especially those belonging to the dimensional regularization (in situations where the method applies). Through an adequate interpretation of the Feynman rules and a convenient representation for involved propagators, the finite and divergent parts are separated before the introduction of the integration in the loop momentum. Only the finite integrals obtained are in fact integrated. The divergent content of the amplitudes are written as a combination of standard mathematical object which are never really integrated. Only very general scale properties of such objects are used. The finite parts, on the other hand, are written in terms of basic functions conveniently introduced. The scale properties of such functions relate them to a well defined way to the basic divergent objects providing simple and transparent connection between both parts in the assintotic regime. All the arbitrariness involved in this type of calculations are preserved in the intermediary steps allowing the identification of universal properties for the divergent integrals, which are required for the maintenance of fundamental symmetries like translational invariance and scale independence in the perturbative amplitudes. Once these consistency relations are imposed no other symmetry is violated in perturbative calculations neither ambiguous terms survive at any theory or model formulated at any space-time dimension including nonrenormalizable cases. Representative examples of perturbative amplitudes involving different species of massive fermions are consid