Crossing-Symmetric Decomposition of then-Point Veneziano Formula into Tree-Graph Integrals. I

Given a cyclic ordering of external particles and ann-point tree Feynman graph T, the tree-graph integral F T is defined in such a way that F T has only the poles relevant to T, that there is a birational transformation by which F T is transformed into an integral identical with the n-point Veneziano formula apart from its integration domain, and that the crossing-symmetry property and Chan's bootstrap condition are manifest. It is proved that the n-point Veneziano formula is written as a sum of FT over all tree graphs T belonging to the given cyclic ordering of external particles.