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I am studying representation theory of Lie groups and its combination to theoretical physics, and I am concerned about the following. Is there an exhaustive way to find all unitary representations of the connected Poincaré Group $SO(1,3)_e\ltimes\mathbb{R}^4$. I am thinking that Mackey Theory that do the trick, but is anyone familiar with other options?

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This is a classical question that was solved by Wigner in "On unitary representations of the inhomogeneous Lorentz group". There is a nice (modern and elementary) exposition in Sternberg's book Group Theory and Physics. This page (from a common contributor here) looks to have a lot of the references.

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