Finitedimensional Feynman DiagramsFeature Column Archive
5. The first appearance of graphsIn the last section we calculated some 2 and 4point functions: <v^{1},v^{2}> = A^{1}_{1,2} <v^{1},v^{1}> = A^{1}_{1,1}<v^{1},v^{2},v^{3},v^{4}> = A^{1}_{2,3}A^{1}_{1,4} + A^{1}_{2,4}A^{1}_{1,3} + A^{1}_{34}A^{1}_{1,2}<v^{1},v^{1},v^{3},v^{4}> = 2 A^{1}_{1,4}A^{1}_{1,3} + A^{1}_{3,4}A^{1}_{1,1} <v^{1},v^{1},v^{1},v^{4}> = 3 A^{1}_{1,4}A^{1}_{1,1} <v^{1},v^{1},v^{4},v^{4}> = 2A^{1}_{1,4}A^{1}_{1,4} + A^{1}_{4,4}A^{1}_{1,1} <v^{1},v^{1},v^{1},v^{1}> = 3 A^{1}_{1,1}A^{1}_{1,1} It is convenient to represent each of products appearing on the right as a graph,where the vertices represent the indices of the coordinatesv^{i} appearing in the mpointfunction, and eachA^{1}_{i,j}becomes an edge from vertex ito vertex j. Here are the graphs correspondingto the terms in the 4point functions above.

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