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Bigravity in Hamiltonian formalism: The tetrad approach

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Abstract

We use the tetrad formalism to calculate a matrix square root occurring in the de Rham-Gabadadze-Tolley potential. In the minimal case, we obtain the constraints and their algebra. We show that the number of gravitational degrees of freedom corresponds to the massless and massive gravity fields. The Boulware-Deser ghost is eliminated because of two second-class constraints.

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References

  1. C. J. Isham, A. Salam, and J. Strathdee, Phys. Lett. B, 31, 300–302 (1970); Phys. Rev. D, 3, 867–873 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  2. B. Zumino, “Effective Lagrangians and broken symmetries,” in: Brandeis University Lectures on Elementary Particles and Quantum Field Theory (S. Deser, M. Grisaru, and H. Pendleton, eds.), Vol. 2, MIT Press, Cambridge, Mass. (1970), pp. 437–500.

    Google Scholar 

  3. T. Damour and I. I. Kogan, Phys. Rev. D, 66, 104024 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  4. C. de Rham, G. Gabadadze, and A. J. Tolley, Phys. Rev. Lett., 106, 231101 (2011); arXiv:1011.1232v2 [hep-th] (2010); Phys. Lett. B, 711, 190–195 (2012); arXiv:1107.3820v1 [hep-th] (2011).

    Article  ADS  Google Scholar 

  5. D. G. Boulware and S. Deser, Phys. Rev. D, 6, 3368–3382 (1972).

    Article  ADS  Google Scholar 

  6. S. F. Hassan and R. A. Rosen, JHEP, 1202, 126 (2012); arXiv:1109.3515v2 [hep-th] (2011).

    Article  ADS  MathSciNet  Google Scholar 

  7. S. F. Hassan and R. A. Rosen, JHEP, 1204, 123 (2012); arXiv:1111.2070v1 [hep-th] (2011).

    Article  ADS  MathSciNet  Google Scholar 

  8. K. Hinterbichler and R. A. Rosen, JHEP, 1207, 047 (2012); arXiv:1203.5783v3 [hep-th] (2012).

    Article  ADS  MathSciNet  Google Scholar 

  9. S. Alexandrov, K. Krasnov, and S. Speziale, JHEP, 1306, 068 (2013); arXiv:1212.3614v2 [hep-th] (2012).

    Article  ADS  MathSciNet  Google Scholar 

  10. S. Alexandrov, Gen. Rel. Grav., 46, 1639 (2014); arXiv:1308.6586v4 [hep-th] (2013).

    Article  ADS  MathSciNet  Google Scholar 

  11. J. Kluson, “Hamiltonian formalism of bimetric gravity in vierbein formulation,” arXiv:1307.1974v3 [hep-th] (2013).

    Google Scholar 

  12. V. O. Soloviev and M. V. Chichikina, Theor. Math. Phys., 176, 1163–1175 (2013); arXiv:1211.6530v3 [hep-th] (2012); V. O. Soloviev and M. V. Tchichikina, Phys. Rev. D, 88, 084026 (2013); arXiv:1302.5096v6 [hep-th] (2013).

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Arnowitt, S. Deser, and Ch. W. Misner, “The dynamics of general relativity,” in: Gravitation: An Introduction to Current Research (L. Witten, ed.), Wiley, New York (1962), pp. 227–265; arXiv:gr-qc/0405109v1 (2004).

    Google Scholar 

  14. K. Kuchař, J. Math. Phys., 17, 777–791, 792–800, 801–820 (1976); 18, 1589–1597 (1977).

    Article  ADS  Google Scholar 

  15. D. Comelli, F. Nesti, and L. Pilo, JHEP, 1307, 161 (2013); arXiv:1305.0236v1 [hep-th] (2013).

    Article  ADS  MathSciNet  Google Scholar 

  16. S. Deser and C. J. Isham, Phys. Rev. D, 14, 2505–2510 (1976); J. E. Nelson and C. Teitelboim, Ann. Phys., 116, 86–104 (1978); M. Henneaux, Gen. Rel. Grav., 9, 1031–1045 (1978).

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute for High Energy Physics, National Research Center “Kurchatov Institute”, Protvino, Moscow Oblast, Russia

    V. O. Soloviev

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  1. V. O. Soloviev
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Correspondence to V. O. Soloviev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 182, No. 2, pp. 350–364, February, 2015.

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Soloviev, V.O. Bigravity in Hamiltonian formalism: The tetrad approach. Theor Math Phys 182, 294–307 (2015). https://doi.org/10.1007/s11232-015-0263-5

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  • DOI: https://doi.org/10.1007/s11232-015-0263-5

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