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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.

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    @Qiaochu: I'm far from a library at the moment, but I'd start looking here: Barut-Rączka, *[Theory of group representations and applications](http://www.ams.org/mathscinet-getitem?mr=495836)*, Sternberg, *[Group theory and physics](http://www.ams.org/mathscinet-getitem?mr=1287387)*, and the books by Mackey.2011-07-12
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    @Theo: thanks for the reference to Sternberg. Looking through it now.2011-07-13
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    @Theo: it seems that Sternberg describes how to construct the representations but doesn't prove that they exhaust the physically meaningful possibilities. Barut-Rączka is extremely thorough but it would take me quite awhile to digest the necessary background...2011-07-13
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    Is it question about irreducible _unitary_ representations?2011-07-17
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    @Alex: yes, I assume so, since that is what Wigner studied.2011-07-18
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    I myself would be glad to know about more general case also ...2011-07-18

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