Abstract
ESSENTIALLY all infinite unitary representations of semi-simple Lie groups are known1, they are of Murray–von Neumann2 type I. Further, while it has been known for a long time that non-relativistic quantum mechanics is such a representation for the rotation group of space3, the same does not carry over to relativistic quantum mechanics. Infinite representations of the Lorentz group4 do not correspond to anything physically identifiable. This, among other things, suggests that the underlying group of relativistic quantum theory is not the Lorentz group but rather one for which non-unitary representations have a special significance.
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