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

Abstract

A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar ${\varphi }^3\oplus {\varphi }^4$ theory, is presented. The representation is obtained starting from an Initial Parameters Matrix (IPM), which relates the scalar products between internal and external momenta, and which appears explicitly when this parametrization is applied to the momentum space representation of the graph. The final product is an algorithm that can be easily programmed, either in a computer programming language (C/C++, Fortran,...) or in a symbolic calculation package (Maple, Mathematica,...).

28 pages, 2 figures

References in corpus (2)

• An automatized algorithm to compute infrared divergent multi-loop integrals
• Numerical evaluation of multi-loop integrals by sector decomposition

Cited by in corpus (6)

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• Definite integrals by the method of brackets. Part 1
• Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams II
• Hypergeometric form of Fundamental theorem of calculus