Cluster properties in relativistic quantum mechanics of N-particle systems

A general technique is presented for constructing a quantum theory of a finite number of interacting particles satisfying Poincare invariance, cluster separability, and the spectral condition. Irreducible representations and Clebsch-Gordan coefficients of the Poincare group are the central elements of the construction. A different realization of the dynamics is obtained for each basis of an irreducible representation of the Poincare group. Unitary operators that relate the different realizations of the dynamis are constructed. This technique is distinguished from other solutions [S. N. Sokolov, Dokl. Akad. Nauk USSR 233, 575 (1977); F. Coester and W. N. Polyzou, Phys. Rev. D 26, 1348 (1982)] of this problem because it does not depend on the kinematic subgroups of Dirac's forms [P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949)] of dynamics. Special basis choices lead to kinematic subgroups. (C) 2002 American Institute of Physics.