Recursive method to obtain the parametric representation of a generic Feynman diagram

Journal Article · Tue Nov 15 04:00:00 EST 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.106006· OSTI ID:20711602

Gonzalez, Ivan; Schmidt, Ivan ^[1]

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1. Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso (Chile)

A recursive algebraic method which allows one to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar {phi}{sup 3}+{phi}{sup 4} theory, is presented. The representation is obtained starting from an initial parameters matrix, which relates the scalar products between internal and external momenta, and which appears directly when this parametrization is applied to the momentum space representation of the graph. The final product is an algebraic formula that shows explicitly the external momenta dependence and also an algorithm that can be easily programmed, either in a computer programming language (C/C++, Fortran, ...) or in a symbolic calculation package (Maple, Mathematica, ...)

• OSTI ID: 20711602
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ALGORITHMS
FEYNMAN DIAGRAM
RECURSION RELATIONS
SCALARS