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The Hamilton-Jacobi analysis and canonical covariant description for three-dimensional Palatini theory plus a Chern-Simons term

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Abstract.

By using the Hamilton-Jacobi (HJ) framework the three-dimensional Palatini theory plus a Chern-Simons term (PCS) is analyzed. We report the complete set of HJ Hamiltonians and a generalized HJ differential from which all symmetries of the theory are identified. Moreover, we show that despite PCS Lagrangian produces Einstein’s equations, the generalized HJ brackets depend on a Barbero-Immirzi-like parameter. In addition we complete our study by performing a canonical covariant analysis, and we construct a closed and gauge invariant two-form that encodes the symplectic geometry of the covariant phase space.

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References

  1. D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints, in Springer Series in Nuclear and Particle Physics (Springer, 1990)

  2. M.B. Green, J.H. Schwarz, E. Witten, Super String Theory (Cambridge University Press, Cambridge, 1986)

  3. J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998)

  4. C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004)

  5. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, 2007)

  6. A. Hanson, T. Regge, C. Teitelboim, Constrained Hamiltonian Systems (Accademia Nazionale dei Lincei, Roma, 1978)

  7. L.D. Faddeev, R. Jackiw, Phys. Rev. Lett. 60, 1692 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  8. E.M.C. Abreu, A.C.R. Mendes, C. Neves, W. Oliveira, F.I. Takakura, L.M.V. Xavier, Mod. Phys. Lett. A 23, 829 (2008)

    Article  ADS  Google Scholar 

  9. E.M.C. Abreu, A.C.R. Mendes, C. Neves, W. Oliveira, F.I. Takakura, Int. J. Mod. Phys. A 22, 3605 (2007)

    Article  ADS  Google Scholar 

  10. E.M.C. Abreu, C. Neves, W. Oliveira, Int. J. Mod. Phys. A 21, 5329 (2008)

    Google Scholar 

  11. C. Neves, W. Oliveira, D.C. Rodrigues, C. Wotzasek, Phys. Rev. D 69, 045016 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  12. C. Neves, C. Wotzasek, Int. J. Mod. Phys. A 17, 4025 (2002)

    Article  ADS  Google Scholar 

  13. C. Neves, W. Oliveira, Phys. Lett. A 32, 267 (2004)

    Article  ADS  Google Scholar 

  14. J.A. Garcia, J.M. Pons, Int. J. Mod. Phys. A 12, 451 (1997)

    Article  ADS  Google Scholar 

  15. E.M.C. Abreu, A.C.R. Mendes, C. Neves, W. Oliveira, R.C.N. Silva, C. Wotzasek, Phys. Lett. A 37, 3603 (2010)

    Article  ADS  Google Scholar 

  16. L. Liao, Y.C. Huang, Ann. Phys. 322, 2469 (2007)

    Article  ADS  Google Scholar 

  17. A. Escalante, J. Manuel-Cabrera, Ann. Phys. 343, 27 (2014)

    Article  ADS  Google Scholar 

  18. A. Escalante, M. Zárate, Ann. Phys. 353, 163 (2015)

    Article  ADS  Google Scholar 

  19. A. Escalante, J. Manuel-Cabrera, Ann. Phys. 36, 1585 (2015)

    Google Scholar 

  20. A. Escalante, O. Rodríguez-Tzompantzi, Ann. Phys. 364, 136 (2016)

    Article  ADS  Google Scholar 

  21. J. Barcelos-Neto, C. Wotzasek, Mod. Phys. Lett. A 7, 1737 (1992)

    Article  ADS  Google Scholar 

  22. J. Barcelos-Neto, C. Wotzasek, Int. J. Mod. Phys. A 7, 4981 (1992)

    Article  ADS  Google Scholar 

  23. C. Crnkovi’c, E. Witten, in Three Hundred Years of Gravitation, edited by S.W. Hawking, W. Israel (Cambridge University Press, Cambridge, 1987)

  24. Y. Güler, J. Math. Phys. 30, 785 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  25. C. Caratheodory, Calculus of Variations and Partial Diferential Equations of the First Order, 3rd edn (American Mathematical Society, 1999)

  26. M.C. Bertin, B.M. Pimentel, C.E. Valcárcel, Ann. Phys. 323, 3137 (2008)

    Article  ADS  Google Scholar 

  27. M.C. Bertin, B.M. Pimentel, C.E. Valcárcel, J. Math. Phys. 55, 112901 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  28. V. Bonzom, E.R. Livine, Class. Quantum Grav. 25, 195024 (2008)

    Article  ADS  Google Scholar 

  29. M. Montesinos, Class. Quantum Grav. 23, 2267 (2006)

    Article  ADS  Google Scholar 

  30. A. Escalante, Phys. Lett. B 676, 105 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  31. A. Escalante, C. Medel-Portugal, Ann. Phys. 391, 27 (2018)

    Article  ADS  Google Scholar 

  32. S. Holts, Phys. Rev. D 53, 5966 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  33. M. Montesinos, Class. Quantum Grav. 18, 1847 (2001)

    Article  ADS  Google Scholar 

  34. D. Jimenez-Rezende, A. Perez, Phys. Rev. D 79, 064026 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  35. A. Escalante, J. Manuel-Cabrera, Ann. Phys. 361, 585 (2015)

    Article  Google Scholar 

  36. A. Escalante, J. Manuel-Cabrera, Eur. Phys. J. C 77, 303 (2017)

    Article  ADS  Google Scholar 

  37. N.T. Maia, B.M. Pimentel, C.E. Valcárcel, Class. Quantum Grav. 32, 185013 (2015)

    Article  ADS  Google Scholar 

  38. A. Escalante, Prihel-Cavildo-Sánchez, Adv. Math. Phys. 2018, 3474760 (2018)

    Article  Google Scholar 

  39. A. Escalante, O. RodrRodríguez-Tzompantzi, J. High Energy Phys. 05, 073 (2014)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla Pue., Mexico

    Alberto Escalante &  Aldair-Pantoja

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  1. Alberto Escalante
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  2. Aldair-Pantoja
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Correspondence to Alberto Escalante.

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Escalante, A., Aldair-Pantoja The Hamilton-Jacobi analysis and canonical covariant description for three-dimensional Palatini theory plus a Chern-Simons term. Eur. Phys. J. Plus 134, 437 (2019). https://doi.org/10.1140/epjp/i2019-12816-6

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