Geodesic
Phase space invariance groups and relativistic three-particle states
Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 1, pp. 85-96 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new approach is proposed to the problem of the classification of the states of three relativistic particles. The method is based on the idea of the existence of a finite group $H$ of transformations that leave invariant not only the equation of the energy surface but also the element of the relativistic three-particle phase volume. Equations are found that determine a one-parametric subgroup of $H$ and, in the case of three identical particles, the group itself is found. An important feature of this group is the fact that the exchange of particles is a particular clement of the group. The Lie algebra of the generators of $H$ are used to construct a complete set of commuting Hermitian operators, including the exchange operator. A complete orthonormalized system of states is obtained; it possesses the necessary symmetry propertics under exchange. The kinematic variables used in the problem map the physical region of the Dalitz plot onto a ring. 
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     author = {G. Yu. Bogoslovskii},
     title = {Phase space invariance groups and relativistic three-particle states},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {85--96},
     year = {1971},
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     number = {1},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1971_8_1_a8/}
}
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G. Yu. Bogoslovskii. Phase space invariance groups and relativistic three-particle states. Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 1, pp. 85-96. http://geodesic.mathdoc.fr/item/TMF_1971_8_1_a8/

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