OK finite dimensional unitary nontrivial representations of the Poincare group don't exist. But suppose that we relax the word 'representation'? We could have a projective representation (or a representation of a central extension) of the Poincare group. There are more general extensions of groups, and representations of these might be thought of as representations of the original group 'up to gauge equivalence' given by the extending group. If anybody could tell me where to look for a discussion of any extended representations, I would be very grateful.

  • $\begingroup$ In the context of quantum mechanics, the unitary representations are always actually projective representations, so the standard Wigner classification already answers your question. $\endgroup$ – ACuriousMind Feb 19 '17 at 12:26
  • $\begingroup$ Thanks. I was hoping that by having more complicated extensions it might be possible to have much smaller representations. Or even just for extended representations of the Lorentz group... $\endgroup$ – Edwin Beggs Feb 19 '17 at 12:50

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