Multidimensional analogues of the geometric s⇆t duality

Customarily, the s <----> t duality property for scattering amplitudes, e.g., for the Veneziano amplitude, is naturally related to two-dimensional geometry. Saito and the author previously proposed a simple geometric construction of such amplitudes. Here, we construct analogues of one such amplitude related to multidimensional Euclidean space; the three-dimensional case is discussed in detail. The result is a variant of the Regge calculus closely related to integrable models.