On the Canonical Relativistic Kinematics of N-Particle Systems

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Abstract
The ``canonical'' relativistic kinematics is discussed for n‐particle systems. Our aim is to derive the formulas in as simple and symmetrical a way as possible and thus to avoid the extra complications arising for n > 2 in the usual stepwise generalization of the two‐particle method. At first we derive the canonical form of the infinitesimal operators (N, M) in a highly symmetrical form. It is then shown that though the restrictions imposed by the condition that our states be also energy eigenstates compel us to sacrifice a part of the symmetry and simplicity of the formulas, we can indeed include the effect of the spins of the component particle in a completely symmetric way. This reduces to a minimum the additional complications introduced when the component particles have nonzero spins. The corresponding, relatively simple, generalized (C‐G) coefficients connecting the canonical and the direct‐product states are calculated. It is shown that the use of ``spinor'' representation for the individual particles simplifies the deductions considerably. Explicit results are given usually for n = 3 only, since the generalization to n > 3 introduces no essentially new features.

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