S@M, a Mathematica Implementation of the SpinorFormalism Page: 4 of 52
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shown in  . Other approaches have combined the knowledge of the generic
structure of loop-integrand [25, 76] with the simplification induced by cut-
constraints, ending up with a unitarity-motivated loop-integral decomposition
[32, 33, 62, 75].
The four-dimensional version of the unitarity method leaves the pure rational-
function terms in the amplitudes undetermined. New approaches to computing
rational terms use an optimized organization of Feynman diagrams, by focus-
ing the standard tensor reduction to tensor integrals which could generate the
rational terms [30, 31].
A recent investigation  on the source of rational terms has been exploring
the idea of their generation via a set of Lorentz-violating counterterms.
Alternatively, these rational functions can be characterized by their kinematic
poles. An efficient means for constructing these terms from their poles and
residues is based on BCFW-like recursion relations [43-47].
The rational parts of amplitudes can be also detected with D-dimensional
unitarity cuts [37,49,58,78,79], and in [49,51] the benefits of four-dimensional
spinorial integration [42,48,50] have been extended to work within the dimen-
sional regularization scheme and with massive particles.
In this paper we present the package SAM (Spinors(IMathematica) which im-
plements the spinor formalism in Mathematica. The package allows the use of
complex-spinor algebra along with the multi-purpose features of Mathematica.
The package provides
" the definitions of the spinor objects with their basic properties,
" functions to manipulate them
" numerical evaluation.
These capabilities make the package S@M suitable for, for example,
- the generation of complex spinors associated with solutions of multi-particle
factorization and of generalized-cut conditions;
- the implementation of BCFW-like recurrence relations for constructing high-
multiplicity tree amplitudes [67,68] and rational coefficients [43-45,80];
- the decomposition of massive momenta onto massless ones, useful for the
implementation of the MHV-rules [81,82] and for the BCFW-shift of mas-
sive legs ;
- the algebraic manipulation of products of tree amplitudes with complex
spinors sewn in unitarity-cuts.
The tool presented here is therefore oriented towards the evaluation of helicity
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Maitre, D. & Mastrolia, P. S@M, a Mathematica Implementation of the SpinorFormalism, article, November 2, 2007; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc890820/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.