Geodesic
Clebsch–Gordan coefficients of the Lorentz group
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 360-367 Cet article a éte moissonné depuis la source Math-Net.Ru

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Gel'fand and Graev's results [1] are used to show that the homogeneous components of the one-particle helical state with zero mass $|k\lambda;\;\rho>(k^2=0)$ form the space of the irreducible representation $\chi(i\rho+\lambda,i\rho-\lambda)$ of the Lorentz group. In a spherical coordinate system it is identical with the space of functions $f(u)$ on the group $U$ of unitary matrices. A decomposition of the space of the direct product of these representations into invariant subspaces is obtained as well as an integral representation for the Clebsch–Gordancoefficients in a canonical basis. 
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     title = {Clebsch{\textendash}Gordan coefficients of the {Lorentz} group},
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I. A. Verdiev. Clebsch–Gordan coefficients of the Lorentz group. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 360-367. http://geodesic.mathdoc.fr/item/TMF_1973_16_3_a8/

[1] I. M. Gelfand, M. I. Graev, Tr. Mosk. matem. ob-va, 11 (1962) | MR | Zbl

[2] M. A. Naimark, Tr. Mosk. matem. ob-va, 8 (1959), 121 | MR

[3] A. Z. Dolginov, I. N. Toptygin, ZhETF, 37 (1959), 1697 | MR | Zbl

[4] G. Bisiacchi, Fronsdal, Nuovo Cim., 41 (1965), 35 | DOI | MR

[5] P. G. Bamberg, preprint 196, Clarendon Lab. Oxford, 1966

[6] R. L. Anderson, R. Raczka, M. A. Rashid, P. Winternitz, J. Math. Phys., 1 (1970), 1050 | DOI | MR | Zbl

[7] M. A. Naimark, Lineinye predstavleniya gruppy Lorentsa, Fizmatgiz, 1958 | MR

[8] I. M. Gelfand, M. I. Graev, N. Ya. Vilenkin, Obobschennye funktsii, t. 5, Fizmatgiz, 1962 | MR

[9] E. P. Wigner, Ann. Math., 40 (1939), 149 | DOI | MR

[10] Yu. M. Shirokov, ZhETF, 33 (1957), 1208 | Zbl

[11] J. S. Lomont, H. E. Moses, J. Math. Phys., 3 (1962), 405 | DOI | MR | Zbl

[12] S. Strom, Arkiv för Fysic, 33 (1967), 465 | MR | Zbl

[13] I. A. Verdiev, YaF, 9 (1969), 1310 | MR