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Teoreticheskaya i Matematicheskaya Fizika, 1970, Volume 4, Number 3, Pages 328–340 (Mi tmf4158)  

This article is cited in 6 scientific papers (total in 6 papers)

Representations of the Lorentz group and generalization of helicity states

Ya. A. Smorodinskii, M. Khusar
References:
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.
Received: 07.10.1969
English version:
Theoretical and Mathematical Physics, 1970, Volume 4, Issue 3, Pages 867–876
DOI: https://doi.org/10.1007/BF01038301
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
\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:
    1. Giorgio Immirzi, “A note on the spinor construction of spin foam amplitudes”, Class. Quantum Grav., 31:9 (2014), 095016  crossref
    2. 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  crossref
    3. K. N. Joshi, B. S. Rajput, “Addition of complex angular momentum operators”, Journal of Mathematical Physics, 21:7 (1980), 1579  crossref
    4. 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  crossref
    5. 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  crossref
    6. 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  mathnet  crossref  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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