Quantizing gravity using physical states of a superstring

B.B. Deo,1 and L. Maharana2


A symmetric zero-mass tensor of rank two is constructed using the superstring modes of excitation, which satisfies the physical state constraints of a superstring. These states have a one to one correspondence with the quantized field operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensor, using the quantum field theory method of quantization. The principle of equivalence makes the tensor identical to the metric tensor at any arbitrary space-time point. The propagator for the quantized field is deduced. The gravitational interaction is switched on by going over from ordinary derivatives to co-derivatives. The Riemann-Christoffel affine connections are calculated, and the weak field Ricci tensor Rmn0 is shown to vanish. The interaction part Rmnint is found, and the exact Rmn of the theory of gravity is expressed in terms of the quantized metric. The quantum-mechanical self-energy of the gravitational field in vacuum is shown to vanish. By the use of a projection operator, it is shown that gravitons are quanta of the general relativity field which gives the Einstein equation Gmn = 0. It is suggested that quantum gravity may be renormalizable by the use of the massless ground state of this superstring theory for general relativity, and a tachyonic vacuum creates and annihilates quanta of quantized gravitational field.


  1. Y. Nambu, Lectures at Copenhagen Symposium (1970).
  2. T. Goto, Prog. Theo. Phys. 46, 1560 (1971).
  3. P. Goddard, J. Goldstone, C. Rebbi and C. B. Thorn, Nucl. Phys. B56, 109 (1973).
  4. P. Goddard, C. Rebbi and C. B. Thorn, Nuovo Cimento. 12, 425 (1972); P. Goddard and C. B. Thorn, Phys. Letts. 40B, 235 (1972).
  5. S. Mandelstam, Phys. Rev. D11, 3026 (1975).
  6. J. Scherk and J. H. Schwarz, Nucl. Phys. B81, 118 (1974); Caltech preprint CALT-58-488 (1975).
  7. J. Scherk and J. H. Schwarz, Phys. Lett. 57B, 463 (1975).
  8. M. B. Green and J. H. Schwarz, Phys. Letts. 136B, 367 (1984).
  9. D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, Nucl. Phys. B256, 253 (1985).
  10. A. Casher, F. Englert, H. Nicolai and A. Taormina, Phys. Lett. B162, 121 (1985).
  11. M. Kaku, Introduction to Superstring Theory and M-theory, 2nd Edn, Springer (1998).
  12. M. Green, J. H. Schwarz and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, England, 1987).
  13. B. B. Deo, Int. J. Mod. Phys. 21A, 237 (2006).
  14. S. Deser and B. Zumino, Phys. Lett. 62B 335 (1976); ibid 65B, 369 (1976).
  15. B. S. DeWitt, Phys. Rev. 162 1195, 1239 (1967); erratum, Phys. Rev. 171, 1834 (1968).
  16. See, e.g., R. N. Mohapatra and P. B. Pal, Massive Neutrinos in Physics and Astrophysics (World Scientific, 1991).
  17. S. James Gates Jr. and W. Siegel, Phys. Letts. B206, 631 (1988); D. A. Depiereux, S. James Gates Jr. and Q-Hann Park, Phys. Letts. B224, 364 (1989); S. Bellucci, D.A. Depiereux and S. James Gates Jr, Phys. Letts. B232, 67 (1989); D. A. Depiereux, S. James Gates Jr and B. Radak, Phys. Letts. B236, 411 (1990).
  18. L. Brink, P. Di Vecchia and P. Howe, Phys. Lett. B65, 471 (1976); S. Deser and B. Zumino, Phys. Lett. B65, 369 (1976).
  19. F. Gliozi, J. Sherk and D. Olive, Nucl. Phys. B122, 253 (1977).
  20. B. B. Deo and L. Maharana, Int. J. Mod. Phys. A20, 99 (2005).
  21. A. Chattaraputi, F. Englert, L. Houart and A. Taormina, J. High Energy Phys. 0209, 037 (2002); A. Chattaraputi, F. Englert, L. Houartand A. Taormina, Class. Quant. Grav. 20, 449 (2003).
  22. J. Polchinski, String Theory, Vol. I, II, (Cambridge University Press, Cambridge, 1998).
  23. J. Polchinski, What is String Theory?, hep-th/9411028.
  24. S. N. Gupta, Proc. Phys. Soc. (London), A63, 681 (1950); K. Bleuler, Helv. Phys. Acta 23, 567 (1950).
  25. T. Padmanabhan, From Gravitons to Gravity: Myths and Reality, gr-qc/0409089.
  26. S. Weinberg, Gravitation and Cosmology (John Wiley & Sons, Inc. New York, 1972).
  27. K. Nishijima, Fields and Particles (W. A. Benjamin Inc., New York, 1969).
  28. J. L. Anderson, Principles of Relativity Physics, (Acadenic Press, New York, 1967).
  29. C. Itzykson and J. Zuber, Quantum Field Theory (McGraw Hill, New York, 1980).
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page