Geodesic
Representations of the Poincar\'e group in $E(2)$~bases
Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 1, pp. 101-119

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Constructions are given of irreducible unitary representations of the quantum-mechanical Poincaré group in two bases associated with the $E(2)$ subgroup for the ease when the square of the mass and the energy are positive, i.e., $M^2>0$ and $P_0>0$. Expressions are found for the generators and the transformation functions from a canonical basis to the $E(2)$ bases are caleuiated. The reduction of a direct product of irreducible representations in an $E(2)$ basis is considered at the end of the paper. 
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Yu. V. Novozhilov; E. V. Prokhvatilov. Representations of the Poincar\'e group in $E(2)$~bases. Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 1, pp. 101-119. http://geodesic.mathdoc.fr/item/TMF_1969_1_1_a7/