Recursive method to obtain the parametric representation of a generic Feynman diagram
Abstract
A recursive algebraic method which allows one to obtain the Feynman or Schwinger parametric representation of a generic Lloops 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, ...)
 Authors:
 Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110V, Valparaiso (Chile)
 Publication Date:
 OSTI Identifier:
 20711602
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.106006; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; ALGORITHMS; FEYNMAN DIAGRAM; RECURSION RELATIONS; SCALARS
Citation Formats
Gonzalez, Ivan, and Schmidt, Ivan. Recursive method to obtain the parametric representation of a generic Feynman diagram. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.106006.
Gonzalez, Ivan, & Schmidt, Ivan. Recursive method to obtain the parametric representation of a generic Feynman diagram. United States. doi:10.1103/PhysRevD.72.106006.
Gonzalez, Ivan, and Schmidt, Ivan. Tue .
"Recursive method to obtain the parametric representation of a generic Feynman diagram". United States.
doi:10.1103/PhysRevD.72.106006.
@article{osti_20711602,
title = {Recursive method to obtain the parametric representation of a generic Feynman diagram},
author = {Gonzalez, Ivan and Schmidt, Ivan},
abstractNote = {A recursive algebraic method which allows one to obtain the Feynman or Schwinger parametric representation of a generic Lloops 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, ...)},
doi = {10.1103/PhysRevD.72.106006},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}

A NEW METHOD FOR INVESTIGATION OF FEYNMAN DIAGRAM SINGULARITIES (in Russian)
The essence of the method is that the diagrams are divided into separate parts whose singularities are known. An equation is derived that expresses the singularity of a diagram as a whole in terms of singularities of the constituents. For a number of diagrams the singularities were determined by the new method as well as by the Landau method. (auth)