Geodesic
$SL(2,R)$ symmetry of dual two-particle amplitude
Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 2, pp. 145-173

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Dispersion relations are used to represent the crossing-symmetric scattering amplitude of two scalar particles as a Mellin integral. The amplitude's duality derives from its being symmetric under irreducible unitary representations of $SL(2,R)$. The symmetry makes it possible to find an integral representation for the dual amplitude, this serving to combine the properties of duality and unitarity. 
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     author = {Kh. D. Popov and D. Ts. Stoyanov and A. N. Tavkhelidze},
     title = {$SL(2,R)$ symmetry of dual two-particle amplitude},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {145--173},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_13_2_a0/}
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Kh. D. Popov; D. Ts. Stoyanov; A. N. Tavkhelidze. $SL(2,R)$ symmetry of dual two-particle amplitude. Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 2, pp. 145-173. http://geodesic.mathdoc.fr/item/TMF_1972_13_2_a0/