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 34 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,...). © 2005 The American Physical Society.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 15 Nov 2005|