Abstract:
The principal series of unitary representations of the Lorentz group is obtained by complexification of the three-dimensional group of rotations and by the solution of the eigenvalue
equation for the Casimir operators. The representation obtained can be expressed simply
in terms of D functions (of the first and second kind) of the group of rotations. The harmonic
analysis of the functions on the group is discussed. Spherical functions on a two-dimensional
complex sphere are constructed.
Citation:
Ya. A. Smorodinskii, M. Khusar, “Representations of the Lorentz group and generalization of helicity states”, TMF, 4:3 (1970), 328–340; Theoret. and Math. Phys., 4:3 (1970), 867–876
\Bibitem{SmoKhu70}
\by Ya.~A.~Smorodinskii, M.~Khusar
\paper Representations of the Lorentz group and generalization of helicity states
\jour TMF
\yr 1970
\vol 4
\issue 3
\pages 328--340
\mathnet{http://mi.mathnet.ru/tmf4158}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=462276}
\zmath{https://zbmath.org/?q=an:0201.58404}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 4
\issue 3
\pages 867--876
\crossref{https://doi.org/10.1007/BF01038301}
Linking options:
https://www.mathnet.ru/eng/tmf4158
https://www.mathnet.ru/eng/tmf/v4/i3/p328
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Sergey N. Filippov, Vladimir I. Man'ko, “Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics”, J Russ Laser Res, 31:3 (2010), 211
K. N. Joshi, B. S. Rajput, “Addition of complex angular momentum operators”, Journal of Mathematical Physics, 21:7 (1980), 1579
M. K. F. Wong, Hsin-Yang Yeh, “Boost matrix elements and Clebsch–Gordan coefficients of the homogeneous Lorentz group”, Journal of Mathematical Physics, 18:9 (1977), 1768
E. G. Kalnins, “Unitary Representations of the Homogeneous Lorentz Group in an O(1,1)⊗O(2) Basis and Some Applications to Relativistic Equations”, Journal of Mathematical Physics, 13:9 (1972), 1304
A. A. Izmest'ev, “Wave fields of beam type and spatial quantization of the angular momentum”, Theoret. and Math. Phys., 7:3 (1971), 591–599