[Math] Irreducible representations of Poincaré group

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I am looking for any reference on Wigner's classification of irreducible representations of the Poincaré group. I know the classification, but is there any reference where the representations are constructed and explained. This classification gives the different spin particles in Quantum mechanics.
Thanks.

Edit (Qiaochu Yuan, 7/12/11): I am also interested in the answer to this question and unsatisfied with the current answer, so I have offered a bounty. I don't currently have institutional access to Wigner's original paper and in any case find it a little difficult to read, and would appreciate a modern, thorough, mathematical account.

Best Answer

You could try to look at:

  • Geometry of Quantum Theory - V. S. Varadarajan - Second Edition, on Chapter 9 (Relativistic Free Particles), in particular to the Theorem 9.4 (p.347), that is the classification theorem obtained by Wigner.
  • A course in abstract harmonic analysis - G. B. Folland, on Chapter 6 (Induced Representations), in particular in the section 6.7.3 (The Poincaré Group, p.190).
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