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Einstein–Cartan–Dirac theory in (1+2)-dimensions

  • Regular Article - Theoretical Physics
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Abstract

Einstein–Cartan theory is formulated in (1+2) dimensions using the algebra of exterior differential forms. A Dirac spinor is coupled to gravity and the field equations are obtained by a variational principle. The space–time torsion is found to be given algebraically in terms of a quadratic spinor condensate field. Circularly symmetric, exact solutions that collapse to AdS 3 geometry in the absence of the Dirac condensate are found.

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References

  1. S. Deser, R. Jackiw, S. Templeton, Ann. Phys. 140, 372 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  2. M. Banados, C. Teitelboim, J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. S. Carlip, Quantum Gravity in (2+1)-Dimensions (Cambridge University Press, Cambridge, 1998)

    Book  MATH  Google Scholar 

  4. A.A. Garcia, F.W. Hehl, C. Heinicke, A. Macias, Phys. Rev. D 67, 124016 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Trautman, Bull. Acad. Pol. Sci. 20, 185, 503, 895 (1972)

    MathSciNet  Google Scholar 

  6. A. Trautman, Einstein–Cartan theory, in Encyclopedia of Mathematical Physics, vol. 2, ed. by J.-P. Francoise, G.L. Naber, S.T. Tsou (Elsevier, Amsterdam, 2006), p. 189. arXiv:gr-qc/0606062 and references therein

    Chapter  Google Scholar 

  7. F.W. Hehl, B.K. Datta, J. Math. Phys. 12, 1334 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  8. T. Dereli, R.W. Tucker, Class. Quantum Gravity 5, 951 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  9. T. Dereli, Y. Obukhov, Phys. Rev. D 62, 0240013 (2000)

    Article  MathSciNet  Google Scholar 

  10. J.D. Brown, J.W. York Jr., Phys. Rev. D 47, 1407 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  11. J.D. Brown, J. Creighton, R.B. Mann, Phys. Rev. D 50, 6394 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  12. M. Hortaçsu, H.T. Özçelik, N. Özdemir, 2+1 dimensional solution of Einstein–Cartan equations. arXiv:0807.4413 [gr-qc]

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Acknowledgement

TD is supported in part by the Turkish Academy of Sciences (TÜBA).

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Authors and Affiliations

  1. Department of Physics, Koç University, 34450, Sarıyer, Istanbul, Turkey

    Tekin Dereli

  2. Department of Physics Engineering, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Neşe Özdemir

  3. Department of Physics, Pamukkale University, 20070, Kınıklı, Denizli, Turkey

    Özcan Sert

Authors
  1. Tekin Dereli
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  2. Neşe Özdemir
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  3. Özcan Sert
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Correspondence to Tekin Dereli.

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Dereli, T., Özdemir, N. & Sert, Ö. Einstein–Cartan–Dirac theory in (1+2)-dimensions. Eur. Phys. J. C 73, 2279 (2013). https://doi.org/10.1140/epjc/s10052-013-2279-z

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  • DOI: https://doi.org/10.1140/epjc/s10052-013-2279-z

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