Geodesic
Trace formula and singularities of the $S$ matrix for a system of three one-dimensional particles. Third group integral
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 2, pp. 247-259

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A new expression is obtained for the third group integral in terms of two- and three-particle $S$ matrices. For Bose and Fermi statisttes, the result is essentially simpler than for Boltzmann statistics. The singularities of the three-particle $S$ matrix are described compactly. The particles are assumed to be one-dimensional. 
@article{TMF_1973_16_2_a10,
     author = {V. S. Buslaev},
     title = {Trace formula and singularities of the $S$ matrix for a system of three one-dimensional particles. {Third} group integral},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {247--259},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_16_2_a10/}
}
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V. S. Buslaev. Trace formula and singularities of the $S$ matrix for a system of three one-dimensional particles. Third group integral. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 2, pp. 247-259. http://geodesic.mathdoc.fr/item/TMF_1973_16_2_a10/