Abstract
Peculiarities of symmetrical quantum systems are considered with the aid of the Mackey's induced representations theory. The four-dimensional coordinate representation of the relativistic quantum mechanics suggested by Stueckelberg in 1941 is rederived, reinterpreted and generalized for an arbitrary spin. Then it is applied to introduce the causal propagator as a particleantiparticle transition amplitude without consideration of a field equation. Finally the theory of relativistic quantum particles interaction is reformulated without an appeal to the concept of quantized fields.
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