A system of (2N−1) first-order linear homogeneous differential equations in each variable is derived for the generalized (with Speer λ parameters) Feynman integrals corresponding to the one-loop graph with N external lines. This system of differential equations is shown to belong to the class studied by Lappo-Danilevsky. A connection with the matrix representation of the monodromy group in all variables is pointed out.
We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields (≤ 4). We then turn our attention to FRA's generated polynomially by one (real) fundamental field, for which a classification is known. Attempting to generalize this result, we describe some connections between FRA's and Graph Theory. The possibility to get new results on the subject following this "graph" approach is briefly discussed.
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