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A systematization for one-loop 4D Feynman integrals

  • O. A. Battistel
  • G. Dallabona
Theoretical Physics

Abstract.

We present a strategy for the systematization of manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one-loop perturbative solutions of QFT, where the use of an explicit regularization is avoided. Two types of systematization are adopted. The divergent parts are put in terms of a small number of standard objects, and a set of structure functions for the finite parts is also defined. Some important properties of the finite structures, specially useful in the verification of relations among Green's functions, are identified. We show that, in fundamental (renormalizable) theories, all the finite parts of two-, three- and four-point functions can be written in terms of only three basic functions while the divergent parts require (only) five objects. The final results obtained within the proposed strategy can be easily converted into those corresponding to any specific regularization technique providing an unified point of view for the treatment of divergent Feynman integrals. Examples of physical amplitudes evaluation and their corresponding symmetry relations verification are presented as well as generalizations of our results for the treatment of Green's functions having an arbitrary number of points are considered.

Keywords

Basic Function Quantum Field Theory Structure Function Arbitrary Number Unify Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • O. A. Battistel
    • 1
  • G. Dallabona
    • 2
  1. 1.Dept. de FísicaUniversidade Federal de Santa MariaSanta MariaBrasil
  2. 2.Universidade Estadual Paulista - Instituto de Física TeóricaSão PauloBrasil

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