QUANTUM-GROUP DESCRIPTION OF DECAYING PARTICLES

The particle decay problem in the random-set approach leads naturally to the q-Poisson distribution. Motivated by the fact that in the class ical quantum mechanical description of particle decay one ends up with a composite system, we construct a Hilbert space using the eigenstate s of the average particle number operator N. In this approach, time is represented by integer multiples of an observation quantum tau. It is shown that these considerations lead to the redefined q-oscillator an d an element of SUq(n) acts like a reversal operator on n time-ordered states.