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in relativistic quantum field theories all particles are members of (unitary) representations of the Poincare group. For massive particles m² > 0 one gets the usual scalar / spinor / vector representations with spin J = 0, 1/2, 1, 3/2, ... and dim. rep. = 2J+1. For massless particles m² = 0 the spin is no longer defined in the usual sense (angular momentum in rest frame does not make sense) and is replaced by helicity. Again one finds the usual representations with dim. rep. = 1 and helicity = +1 and -1, respectively.

Question: what happens for m² < 0? how do the representations look like and why are they unphysical?

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# Representations of the Poincare group

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