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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