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 DD 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
This publication is cited in the following 6 articles:
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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
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