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Foundations of Physics

, Volume 40, Issue 7, pp 867–899 | Cite as

A Review About Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry

  • S. CapozzielloEmail author
  • M. De Laurentis
Article

Abstract

In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of matter, gauge fields (and then spin connections). After we show, in a self-contained approach, how the tetrads and the Lorentz group can be used to induce the spacetime metric and then the Invariance Induced Gravity can be directly obtained both in holonomic and anholonomic pictures. Besides, we show how tensor valued connection forms act as auxiliary dynamical fields associated with the dilation, special conformal and deformation (shear) degrees of freedom, inherent to the bundle manifold. As a result, this allows to determine the bundle curvature of the theory and then to construct boundary topological invariants which give rise to a prototype (source free) gravitational Lagrangian. Finally, the Bianchi identities, the covariant field equations and the gauge currents are obtained determining completely the dynamics.

Gauge symmetry Conformal-affine Lie algebra Gravity Fiber bundle formalism 

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References

  1. 1.
    Utiyama, R.: Phys. Rev. 101, 1597 (1956) zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Yang, C.N., Mills, R.L.: Phys. Rev. 96, 191 (1954) CrossRefMathSciNetADSGoogle Scholar
  3. 3.
    Kibble, T.W.: J. Math. Phys. 2, 212 (1960) CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Cartan, E.: Ann. Ec. Norm. 42, 17 (1925) MathSciNetADSGoogle Scholar
  5. 5.
    Sciama, D.W.: On the analog between charge and spin in General Relativity. In: Recent Developments in General Relativity, Festschrift for Leopold Infeld, p. 415. Pergamon, New York (1962) Google Scholar
  6. 6.
    Finkelstein, R.: Ann. Phys. 12, 200 (1961) zbMATHCrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Hehl, F.W., Datta, B.K.: J. Math. Phys. 12, 1334 (1971) CrossRefMathSciNetADSGoogle Scholar
  8. 8.
    Hehl, F.W., von der Heyde, P., Kerlick, G.D., Nester, J.M.: Rev. Mod. Phys. 48, 393 (1976) CrossRefADSGoogle Scholar
  9. 9.
    Mansouri, F., Chang, L.N.: Phys. Rev. D 13, 3192 (1976) CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Mansouri, F.: Phys. Rev. Lett. 42, 1021 (1979) CrossRefADSGoogle Scholar
  11. 11.
    Grignani, G., Nardelli, G.: Phys. Rev. D 45, 2719 (1992) CrossRefMathSciNetADSGoogle Scholar
  12. 12.
    Chang, L.N., Macrae, K.I., Mansouri, F.: Phys. Rev. D 13, 235 (1976) CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Hehl, F.W., McCrea, J.D.: Found. Phys. 16, 267 (1986) CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    Capozziello, S., Cianci, R., Stornaiolo, C., Vignolo, S.: Class. Quantum Gravity 24, 6417 (2007) zbMATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    Capozziello, S., Cianci, R., Stornaiolo, C., Vignolo, S.: Int. J. Geom. Methods Mod. Phys. 5, 765 (2008) CrossRefMathSciNetGoogle Scholar
  16. 16.
    Magnano, G., Ferraris, M., Francaviglia, M.: Class. Quantum Gravity 7, 557 (1990) zbMATHCrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Inomata, A., Trikala, M.: Phys. Rev. D 19, 1665 (1978) CrossRefADSGoogle Scholar
  18. 18.
    Callan, C.G., Coleman, S., Wess, J., Zumino, B.: Phys. Rev. 117, 2247 (1969) CrossRefADSGoogle Scholar
  19. 19.
    Coleman, S., Wess, J., Zumino, B.: Phys. Rev. 117, 2239 (1969) CrossRefADSGoogle Scholar
  20. 20.
    Isham, C.J., Salam, A., Strathdee, J.: Ann. Phys. 62, 98 (1971) zbMATHCrossRefMathSciNetADSGoogle Scholar
  21. 21.
    Salam, A., Strathdee, J.: Phys. Rev. 184, 1750 (1969) CrossRefMathSciNetADSGoogle Scholar
  22. 22.
    Salam, A., Strathdee, J.: Phys. Rev. 184, 1760 (1969) CrossRefMathSciNetADSGoogle Scholar
  23. 23.
    Borisov, A.B., Ogievetskii, V.I.: Theor. Mat. Fiz. 21, 329 (1974) Google Scholar
  24. 24.
    Ivanov, E.A., Ogievetskii, V.I.: Gauge theories as theories of spontaneous breakdown. Preprint of the Joint Institute of Nuclear Research, E2-9822, pp. 3–10 (1976) Google Scholar
  25. 25.
    Chang, L.N., et al.: Phys. Rev. D 17, 3168 (1978) CrossRefMathSciNetADSGoogle Scholar
  26. 26.
    Stelle, K.S., et al.: Phys. Rev. D 21, 1466 (1980) CrossRefMathSciNetADSGoogle Scholar
  27. 27.
    Ivanov, E.A., Niederle, J.: Phys. Rev. D 25, 976 (1982) CrossRefMathSciNetADSGoogle Scholar
  28. 28.
    Ivanov, E.A., Niederle, J.: Phys. Rev. D 25, 988 (1982) CrossRefMathSciNetADSGoogle Scholar
  29. 29.
    Ivanenko, D., Sardanashvily, G.A.: Phys. Rep. 94, 1 (1983) CrossRefMathSciNetADSGoogle Scholar
  30. 30.
    Capozziello, S., De Laurentis, M.: Int. J. Geom. Methods Mod. Phys. 6, 1 (2009) zbMATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Basini, G., Capozziello, S.: Gen. Relativ. Gravit. 35, 2217 (2003) zbMATHCrossRefMathSciNetADSGoogle Scholar
  32. 32.
    Basini, G., Capozziello, S.: Int. J. Mod. Phys. D 15, 583 (2006) zbMATHCrossRefMathSciNetADSGoogle Scholar
  33. 33.
    Lord, A., Goswami, P.: J. Math. Phys. 27, 3051 (1986) zbMATHCrossRefMathSciNetADSGoogle Scholar
  34. 34.
    Lord, E.A., Goswami, P.: J. Math. Phys. 29, 258 (1987) CrossRefMathSciNetADSGoogle Scholar
  35. 35.
    Ne’eman, Y., Regge, T.: Riv. Nuovo Cimento 1, 1 (1978) MathSciNetGoogle Scholar
  36. 36.
    Ne’eman, Y., Sijacki, D.: Gravity from symmetry breakdown of a gauge affine theory. The Center for Particle Theory, University of Texas at Austin, D6-87/40 (1987) Google Scholar
  37. 37.
    Lopez-Pinto, A., Tiemblo, A., Tresguerres, R.: Class. Quantum Gravity 12, 1503 (1995) zbMATHCrossRefMathSciNetADSGoogle Scholar
  38. 38.
    Julve, J., et al.: Class. Quantum Gravity 12, 1327 (1995) CrossRefMathSciNetADSGoogle Scholar
  39. 39.
    Tresguerres, R., Mielke, E.W.: Phys. Rev. D 62, 044004 (2000) CrossRefMathSciNetADSGoogle Scholar
  40. 40.
    Tresguerres, R.: Phys. Rev. D 66, 064025 (2002) CrossRefMathSciNetADSGoogle Scholar
  41. 41.
    Capozziello, S., Stornaiolo, C.: Int. J. Geom. Methods Mod. Phys. 5, 185 (2008) CrossRefMathSciNetGoogle Scholar
  42. 42.
    Tiemblo, A., Tresguerres, R.: Gravitational contribution to fermion masses. Eur. Phys. J. C 42, 437 (2005). arXiv:gr-qc/0506034 CrossRefADSGoogle Scholar
  43. 43.
    Tiemblo, A., Tresguerres, R.: Recent Res. Dev. Phys. 5, 1255 (2004) Google Scholar
  44. 44.
    Schwarz, A.: Topology for Physicists. Springer-Verlag, Berlin/Heidelberg (1994) zbMATHGoogle Scholar
  45. 45.
    Nakahara, M.: Geometry, Topology and Physics. Graduate Student Series in Physics, 2nd edn. Institute of Physics, Bristol (2003) zbMATHGoogle Scholar
  46. 46.
    Tiemblo, A., Tresguerres, R.: Time evolution in dynamical spacetimes. arXiv:gr-qc/9607066
  47. 47.
    Giachetta, G.: J. Math. Phys. 40, 939 (1999) zbMATHCrossRefMathSciNetADSGoogle Scholar
  48. 48.
    Cacciatori, S.L., Caldarelli, M.M., Giacomini, A., Klemm, D., Mansi, D.S.: J. Geom. Phys. 56, 2523 (2006) zbMATHCrossRefMathSciNetADSGoogle Scholar
  49. 49.
    Tresguerres, R.: J. Math. Phys. 33, 4231 (1992) zbMATHCrossRefMathSciNetADSGoogle Scholar
  50. 50.
    Scipioni, R.: Class. Quantum Gravity 16, 2471 (1999) zbMATHCrossRefMathSciNetADSGoogle Scholar
  51. 51.
    Seiberg, N.: Emergent Spacetime, Rapporteur talk at the 23rd Solvay Conference in Physics, December, 2005. arXiv:hep-th/0601234
  52. 52.
    Capozziello, S., Lambiase, G., Stornaiolo, C.: Ann. Phys. (Leipzig) 10, 713 (2001) zbMATHCrossRefMathSciNetADSGoogle Scholar
  53. 53.
    Nojiri, S., Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4, 115 (2007) zbMATHCrossRefMathSciNetGoogle Scholar
  54. 54.
    Capozziello, S., Francaviglia, M.: Gen. Relativ. Gravit. 40, 357 (2008) zbMATHCrossRefMathSciNetADSGoogle Scholar
  55. 55.
    Sotiriou, T.P., Faraoni, V.: Phys. Rep. (2009, in press). arXiv:0805.1726 [gr-qc]

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dipartimento di Scienze FisicheUniversità di Napoli “Federico II”NapolyItaly
  2. 2.INFN Sez. di NapoliCompl. Univ. Monte S. AngeloNapoliItaly

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