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 TMF, 1971, Volume 8, Number 1, Pages 85–96 (Mi tmf4387)

Phase space invariance groups and relativistic three-particle states

G. Yu. Bogoslovskii

Abstract: 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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English version:
Theoretical and Mathematical Physics, 1971, 8:1, 690–698

Citation: G. Yu. Bogoslovskii, “Phase space invariance groups and relativistic three-particle states”, TMF, 8:1 (1971), 85–96; Theoret. and Math. Phys., 8:1 (1971), 690–698

Citation in format AMSBIB
\Bibitem{Bog71} \by G.~Yu.~Bogoslovskii \paper Phase space invariance groups and relativistic three-particle states \jour TMF \yr 1971 \vol 8 \issue 1 \pages 85--96 \mathnet{http://mi.mathnet.ru/tmf4387} \transl \jour Theoret. and Math. Phys. \yr 1971 \vol 8 \issue 1 \pages 690--698 \crossref{https://doi.org/10.1007/BF01038678} 

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This publication is cited in the following articles:
1. G. Yu. Bogoslovskii, “On the integration of infinitesimal transformations of the relativistic quasiexchange group”, Theoret. and Math. Phys., 11:2 (1972), 454–459
2. G. I. Garas'ko, N. P. Klepikov, “Justification of partial-wave expansions of relativistic many-particle amplitudes”, Theoret. and Math. Phys., 31:2 (1977), 402–408
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