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Variational theory of an ideal spin liquid in the quadratic theory of gravitation in a Riemann-Cartan space

  • Elementary Particle Physics and Field Theory
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Soviet Physics Journal Aims and scope

Abstract

A variational theory of an ideal Weyssenhoff-Raabe spin liquid in a Riemann-Cartan space is constructed in the metric theory of gravitation (taking into account the quadratic invariants in the Lagrangian). The couplings which arise in the theory and are imposed on the dynamical variables are taken into account in the action integral with the help of the method of undetermined Lagrange multipliers. The canonical energy-momentum tensor of an ideal spin liquid arises in a natural manner as a source on the right side of the gravitational field equations.

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Literature cited

  1. J. Weyssenhoff and A. Raabe, Acta Phys. Polon.,9, 7 (1947).

    Google Scholar 

  2. E. Halbwachs, Theorie Relativiste des Fluides a Spin, Gauthier-Villars, Paris (1960).

    Google Scholar 

  3. L. I. Sedov, Mechanics of Continuous Media [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  4. V. A. Zhelnorovich, Models of Continuous Media Having Internal Electromagnetic and Mechanical Moments [in Russian], Moscow (1980).

  5. G. A. Maugin and A. C. Eringen, J. Math. Phys.,13, 1788 (1972).

    Google Scholar 

  6. A. V. Minkevich and F. Karakura, J. Phys. A,16, 1409 (1983).

    Google Scholar 

  7. O. V. Baburova, V. N. Ponomarev, and B. N. Frolov in: Abstracts of Reports at the All-Union Conference on “Modern Theoretical and Experimental Problems in the Theory of Relativity and Gravitation,” UDN Press, Moscow (1984), p. 307.

    Google Scholar 

  8. V. N. Tunyak, Dokl. Akad. Nauk BSSR,19, 599 (1975).

    Google Scholar 

  9. J. R. Ray and L. L. Smally, Phys. Rev. D,27, 1383 (1983).

    Google Scholar 

  10. R. De Ritis et al., Phys. Rev. D,28, 713 (1983).

    Google Scholar 

  11. N. Salie, Czech. J. Phys. B,24, 831 (1974).

    Google Scholar 

  12. B. N. Frolov in: Modern Problems in Gravitation [in Russian], Tbilisi University Press, Tbilisi (1967), p. 270.

    Google Scholar 

  13. K. Hayashi, Progr. Theor. Phys.,39, 494 (1968).

    Google Scholar 

  14. W. Korczynski, Bull. Acad. Pol. Sci., Ser. Math. Astron. Phys.,23, 467 (1975).

    Google Scholar 

  15. A. A. Tseitlin and V. N. Ponomarev, Vestn. Mosk. Univ., Ser. Fiz. Astron.,19, No. 6, 57 (1978).

    Google Scholar 

  16. V. N. Ponomarev, A. O. Barvinskii, and Yu. N. Obukhov, Geometrodynamic Methods and the Gauge Approach to the Theory of Gravitational Interactions [in Russian], Énergoatomizdat, Moscow (1985).

    Google Scholar 

  17. F. W. Hehl, P. Heyde, G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys.,48, 393 (1976).

    Google Scholar 

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Authors and Affiliations

  1. V. I. Lenin Moscow Pedagogical Institute, USSR

    O. V. Baburova

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  1. O. V. Baburova
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Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 10, pp. 101–105, October, 1989.

In conclusion I thank Professor V. N. Ponomarev and B. N. Frolov for their constant interest in this work and for a discussion of the results.

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Baburova, O.V. Variational theory of an ideal spin liquid in the quadratic theory of gravitation in a Riemann-Cartan space. Soviet Physics Journal 32, 849–853 (1989). https://doi.org/10.1007/BF00898321

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  • DOI: https://doi.org/10.1007/BF00898321

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