Title:ON THE STRUCTURE OF THE SUPPLEMENTARY SERIES OF
UNITARY IRREDUCIBLE REPRESENTATIONS OF THE PROPER, ORTOCHRONOUS
LORENTZ GROUP
Authors:A.Staruszkiewicz (Institute of Physics, Jagellonian
University, Reymonta 4, 30-059 Krak\'ow, Poland)
Representations from the supplementary series of unitary irreducible representations of the proper, ortochronous Lorentz group are labelled by the parameter $z$, $0<z<1$. There are qualitative differences between representations with $0<z<1/2$ and those with $1/2<z<1$. Two such differences are described in this paper: the probability density of parabolic rotations in a spherically symmetric state is singular at the origin for $0<z<1/2$ but regular for $1/2<z<1$; the Casimir operator of the little group, which preserves a space-like vector, has for $0<z<1/2$ a bound state which disappears for $1/2<z<1$.
Key words: Lorentz group, unitary representations
Comments: Figs. 0, Refs. 6, Tabs. 0.
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