Recursive method to obtain the parametric representation of a generic Feynman diagram
نویسنده
چکیده
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 φ⊕φ 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,...). PACS: 11.25 Db; 12.38 Bx
منابع مشابه
Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams II
A modular application of the integration by fractional expansion method for evaluating Feynman diagrams is extended to diagrams that contain loop triangle subdiagrams in their geometry. The technique is based in the replacement of this module or subdiagram by its corresponding multiregion expansion (MRE), which in turn is obtained from Schwinger’s parametric representation of the diagram. The r...
متن کاملA new method for the calculation of massive multiloop diagrams
Starting from the parametric representation of a Feynman diagram, we obtain it’s well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a representation consisting of well-defined compact integrals. The result is a simple transformation of the integrand which gives the analytic continuation of a wide cl...
متن کاملModular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams
We present an alternative technique for evaluating multiloop Feynman diagrams, using the integration by fractional expansion method. Here we consider generic diagrams that contain propagators with radiative corrections which topologically correspond to recursive constructions of bubble type diagrams. The main idea is to reduce these subgraphs, replacing them by their equivalent multiregion expa...
متن کاملRecursive technique for evaluation of Feynman diagrams
A method is presented in which matrix elements for some processes are calculated recursively. This recursive calculational technique based on the method of basis spinor.
متن کاملGeneralization of general helices and slant helices
In this work, we use the formal definition of $k$-slant helix cite{ali2} to obtain the intrinsic equations as well as the position vector for emph{slant-slant helices} which a generalization of emph{general helices} and emph{slant helices}. Also, we present some characterizations theorems for $k$-slant helices and derived, in general form, the intrinsic equations for such curves. Thereafter, fr...
متن کامل