Abstract
A simple and concrete example for illustrating the properties of noncompact groups is presented. This example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. It is shown that the lack of unitarity in a finite-dimensional representation corresponds to a Lorentz contraction of total probability. This paper gives a group-theoretical review of the oscillator formalism which was presented previously as a calculational tool for high-energy physics.
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