Geodesic
Impact parameter representations from the point of view of the Poincaré group
Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 3, pp. 407-421 Cet article a éte moissonné depuis la source Math-Net.Ru

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Impact parameter representations for the two-particle scattering amplitude are derived by expanding the two-particle state with respect to groups that are isomorphic to the group of motions of the plane $E(2)$. The generators of these groups are expressed in terms of the operators of the total angular momentum and the relative momentum of two particles, As a result, the impact parameter operator and states of two particles with definite impact parameter acquire a meaning in terms of the Poincaré group. 
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     author = {A. A. Andrianov},
     title = {Impact parameter representations from the point of view of the {Poincar\'e} group},
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A. A. Andrianov. Impact parameter representations from the point of view of the Poincaré group. Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 3, pp. 407-421. http://geodesic.mathdoc.fr/item/TMF_1973_17_3_a8/

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