Geodesic
Multidimensional analogues of the geometric $s\leftrightarrow t$ duality
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 169-176
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Customarily, the $s\leftrightarrow t$ 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 spaces; the three-dimensional case is discussed in detail. The result is a variant of the Regge calculus closely related to integrable models. 
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I. G. Korepanov. Multidimensional analogues of the geometric $s\leftrightarrow t$ duality. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 169-176. http://geodesic.mathdoc.fr/item/TMF_2000_124_1_a10/

[1] A. E. Kennelly, Electrical World and Engineer, 34 (1899), 413–414

[2] R. M. Kashaev, On discrete $3$-dimensional equations associated with the local Yang–Baxter relation, Preprint ENSLAPP-L-569/95, ENS-Lyon, Lyon, 1995 ; E-print solv-int/9512005 | MR

[3] R. M. Kashaev, I. G. Korepanov, S. M. Sergeev, TMF, 117:3 (1998), 370–384 | DOI | MR | Zbl

[4] I. G. Korepanov, Zap. nauchn. semin. POMI, 215, 1994, 178–196

[5] I. G. Korepanov, Algebraic integrable systems, $(2+1)$-dimensional models in wholly discrete space-time, and inhomogeneous models in $2$-dimensional statistical physics, E-print solv-int/9506003

[6] I. G. Korepanov, S. Saito, TMF, 120:1 (1999), 54–63 | DOI | MR | Zbl

[7] M. Grin, Dzh. Shvarts, E. Vitten, Teoriya superstrun, T. 1, Mir, M., 1990 | MR | Zbl

[8] M. Berzhe, Geometriya, T. 1, 2, Mir, M., 1984 | MR

[9] Ch. Mizner, K. Torn, Dzh. Uiler, Gravitatsiya, T. 3, Mir, M., 1977 | MR

[10] I. G. Korepanov, The tetrahedral analog of Veneziano amplitude, E-print solv-int/9904005