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Generation of modes on the three-dimensional sphere

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Abstract

We use the method of Lie generation of tensor fields, which works for fields of different tensor structures, to construct the complete system of scalar, vector, symmetric tensor, and spinor fields on the three-dimensional sphere. We construct the Pauli operator explicitly. We demonstrate the role of spin in forming the mode series.

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References

  1. B. Riemann, Nachr. K. Ges. Wiss. Göttingen, 13, 133 (1868).

    Google Scholar 

  2. A. Friedmann, Z. Phys., 10, 377 (1922).

    Article  Google Scholar 

  3. K. Land and J. Magueijo, Phys. Rev. Lett., 95, 071301 (2005); astro-ph/0502237 (2005).

    Google Scholar 

  4. B. Mashhoon, Phys. Rev. D, 8, 4297 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  5. E. M. Lifshitz, Zh. Eksp. Teor. Fiz., 16, 587 (1946).

    MathSciNet  Google Scholar 

  6. H. Kodama, “Behavior of cosmological perturbations in the brane-world mode,” in: Cosmology and Particle Physics: CAPP 2000, Verbier, Switzerland 17–28 July 2000 (AIP Conf. Proc., Astron. Astrophys., Vol. 555, R. Durrer, J. Garcia-Bellido, and M. Shaposhnikov), Springer, Berlin (2001), p. 539; hep-th/0012132 (2000).

    Google Scholar 

  7. V. F. Mukhanov, L. R. W. Abramo, and R. H. Branderberger, Phys. Rev. Lett., 78, 1624 (1997).

    Article  ADS  Google Scholar 

  8. D. E. Burlankov, Dynamics of Space [in Russian], Nizhni Novgorod State Univ. Publ., Nizhni Novgorod (2005).

    Google Scholar 

  9. V. Fock, Z. Phys., 98, 145 (1935); “Hydrogen atom and non-Euclidean geometry,” in: Selected Papers [in Russian], St. Petersburg State Univ., St. Petersburg (2003), p. 159.

    Article  MATH  Google Scholar 

  10. N. Ya. Vilenkin, Special Functions and the Theory of Group Representations [in Russian], Nauka, Moscow (1965); English transl., Amer. Math. Soc., Providence, R. I. (1968).

    Google Scholar 

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Authors and Affiliations

  1. Nizhni Novgorod State University, Nizhni Novgorod, Russia

    D. E. Burlankov

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  1. D. E. Burlankov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 417–440, March, 2007.

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Burlankov, D.E. Generation of modes on the three-dimensional sphere. Theor Math Phys 150, 355–376 (2007). https://doi.org/10.1007/s11232-007-0027-y

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  • DOI: https://doi.org/10.1007/s11232-007-0027-y

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