Dual Amplitudes and Basic Assumptions

Four simple assumptions for scattering amplitudes are proposed in order to derive dual amplitudes. The assumptions are conventional except the one which states that each term of an amplitude, corresponding to a certain combination of Regge poles ins, t and u channels, is constructed by a triple product form of three unknown functions, U1 (t), {12 (s) and us (u). This is arrived at by an abstraction from Virasoro type amplitudes. These assumptions lead to difference equations for g's, which can be solved. It is found that the amplitude can be uniquely determined and that it coincides with the amplitudes of Virasoro type and with the ones of Veneziano type when the sums of the trajectories in s, t and u channels are determined by isospin crossing considerations. Examples are given for nn~n(J) scattering and nN~nN scattering. For the latter, it is shown that the A amplitude (in usual notation) obtained coincides with the one proposed by lgi and Hara, but B does not. It is concluded that some daughter trajectories of N and J must contribute to the B amplitude. Also our basic assumptions generally exclude the terms with P', Nand J trajectories for the A amplitude and the terms with p, Nand J trajectories for the B amplitude, which suggests possible existence of some kinds of selection rules.