Linear Dependences and the Multiloop Veneziano Amplitude

By using the identities of Brower and Weis, several apparent inconsistencies associated with twisting the Sciuto three-Reggeon vertex are clarified. By using these results, all linear dependences are eliminated from planar, nonplanar, and overlapping n-loop amplitudes and shown to have only a minor effect. The Thorn projection operator is reduced to a hypergeometric function in the number operator and finally to a rational function. The equivalence of these techniques with the projected propagator of Gross and Schwarz and Ida is demonstrated.