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My understanding is that when it comes to the correspondence between representation theory and particle physics, every irreducible representation of the Poincare group has a corresponding fundamental particle.

My questions are as follows:

  1. are all of the currently known fundamental particles predicted to exist by this correspondence idea?

  2. does the traditional $ISO(3,1)$ Poincare group/algebra predict the existence of supersymmetric particles? If not, what superalgebra is needed?

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    $\begingroup$ To clarify: Wigner's classification doesn't predict the existence of particles. It only classifies whatever particles happen to exist. Can questions 1 and 2 be re-worded in a way that still makes sense after that clarification? (For example, 1. do all of the currently known fundamental particles respect Wigner's classification?) $\endgroup$ – Chiral Anomaly May 31 at 15:49
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  1. No, the Poincare symmetry only predicts relationships between different inertial frames.

  2. Again no. One would need a supersymmetric extension of the Poincare group.

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