# 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 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, ...)

- Authors:

- Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, 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 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, ...)},

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}

}