I am reading texts on QFT and they place a lot of emphasis on finding irreducible representations of the Lorentz/Poincare Group. I also recall some level of discussion from non-relativistic quantum mechanics, and I've also read up a bit on them in texts on representation theory. I am wondering however why they are particularly significant to physicists. If anyone could clarify this for me it would be greatly appreciated.
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Is the question about the theory of representation, or about the irreducible representation of group theory ? – FraSchelle Nov 29 '17 at 09:45
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An irreducible representation indicates that the quantum system is elementary; please see the following question: https://physics.stackexchange.com/questions/73593/why-do-we-say-that-irreducible-representation-of-poincare-group-represents-the-o – David Bar Moshe Dec 03 '17 at 15:21