Graphical Representation of SUSY and Application to QFT

We present a graphical representation of the supersymmetry and the graphical calculation. Calculation is demonstrated for 4D Wess-Zumino model and for Super QED. The chiral operators are graphically expressed in an illuminating way. The tedious part of SUSY calculation, due to manipulating chiral suffixes, reduces considerably. The application is diverse. PACS. 02.10.Ox Copmbinatorics, graph theory – 02.70.-c Computational techniques, ... The supersymmetry is the symmetry between fermions and bosons. It was introduced in the mid 70’s. At present the experiment does not yet confirm the symmetry, but everybody accepts its importance in nature and expects fruitful results in the future developement. The requirement of such a high symmetry costs a sophisticated structure which makes its dynamical analysis difficult. In this circumstance, we propose a calculational technique which utilizes the graphical representation of SUSY. The representation was proposed in [1,2]. 1 The spinor is represented as a slanted line with a direction. Its chirality is represented by the way the line is drawn. The advantage of the graph expression is the use of the graph indices. Every independent graph, which corresponds to a unique term in the ordinary calculation, is classified by a set of graph indices. Hence the main efforts of programinng is devoted to find good graph indices and to count them. SUSY calculation generally is not a simple algebraic or combinatoric or analytical one. It involves the vast branch of mathematics including Grassmann algebra. The delicate property of chirality is produced in this environment. It requires a basic language for flexible programming. We take C-language and present the output of a first-step program. Weyl spinors have the SU(2)L×SU(2)R structure. The chiral suffix α, appearing in ψ or ψα, represents (fundamental representation, doublet representation) SU(2)L and the anti-chiral suffix α̇, appearing in ψ̄ or ψ̄α̇, represents SU(2)R. The raising and lowering of suffixes are done by the antisymmetric tensors ǫ and ǫαβ.