Conformally and gauge invariant spin-2 field equations

C.S.O. Mayor, G. Otalora, J.G. Pereira1


Using an approach based on the Casimir operators of the de Sitter group, conformally invariant equations for a fundamental spin-2 field are obtained, and their consistency is discussed. It is shown that only when the spin-2 field is interpreted as a 1-form assuming values in the Lie algebra of the translation group, rather than a symmetric second-rank tensor, the field equation is both conformally and gauge invariant.


  1. See, e.g., R.M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
  2. S. Deser and R. I. Nepomechie, Ann. Phys. (N.Y.) 154, 396 (1984).
  3. V. WA?nsch, Math. Nachr. 129, 269 (1986).
  4. V. P. Gusynin and V. V. Romanaˆ™kov, Sov. J. Nucl. Phys. 46, 1097 (1987).
  5. C. Aragone and S. Deser, Nuovo Cim. A 3, 4 (1971); ibid., B 57, 33 (1980).
  6. H. I. Arcos, Tiago Gribl Lucas, and J. G. Pereira, Class. Quantum Grav. 27, 145007 (2010); Arxiv: 1001.3407.
  7. S. Weinberg, The Quantum Theory of Fields, Vol. 1 (Cambridge University Press, Cambridge, 1995), p. 254.
  8. J. Erdmenger and H. Osborn, Class. Quantum Grav. 15, 273 (1998); gr-qc/9708040.
  9. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973).
  10. F. GA?rsey, in: Group Theoretical Concepts and Methods in Elementary Particle Physics, ed. by F. GA?rsey, Istanbul Summer School of Theoretical Physics (Gordon and Breach, New York, 1962).
  11. R. Aldrovandi and J. G. Pereira, An Introduction to Geometrical Physics (World Scientific, Singapore, 1995).
  12. C. G. Callan, S. Coleman, and R. Jackiw, Ann. Phys. (N.Y.) 59, 42 (1970).
  13. R. Aldrovandi, J. P. BeltrA?n Almeida, and J. G. Pereira, Class. Quantum Grav. 24, 1385 (2007); gr-qc/0606122.
  14. N. D. Birrel and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982).
  15. J. Dixmier, Bul. Soc. Math. Fran. 89, 9 (1961).
  16. R. Aldrovandi and J. G. Pereira, Teleparallel Gravity: An Introduction (Springer, Dordrecht, 2012).
  17. P. A. M. Dirac, in: Planck Festscrift, ed. by B. Kockel, W. Macke, and A. Papapetrou (Deutscher Verlag der Wissenschaften, Berlin, 1958).
  18. S. Deser and M. Henneaux, Class. Quantum Grav. 24, 1683 (2007); gr-qc/0611157.
  19. M. Fierz and W. Pauli, Proc. Roy. Soc. Lond. A 173, 211 (1939).
  20. Yu. N. Obukhov and J. G. Pereira, Phys. Rev. D 67, 044008 (2003); gr-qc/0212078.
  21. H. I. Arcos, C. S. O. Mayor, G. OtA?lora, and J. G. Pereira, Found. Phys. 42, 1339 (2012); arXiv: 1110.3288.
  22. S. Vilasi, G. Sparano, and G. Vilasi, Class. Quantum Grav. 28, 195014 (2011); arXiv: 1009.3849.
  23. K. Peeters, Introducing Cadabra: A symbolic computer algebra system for field theory problems, hep-th/0701238.
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page