Quantum Gravity in Heisenberg Representation and Self-Consistent Theory of Gravitons in Macroscopic Spacetime

Affiliation(s)

Research Institute of Physics, Southern Federal University, Rostov-on-Don, Russia.

Physics Department, University of Maryland, East West Space Science Center, College Park, USA.

Research Institute of Physics, Southern Federal University, Rostov-on-Don, Russia.

Physics Department, University of Maryland, East West Space Science Center, College Park, USA.

ABSTRACT

The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically equivalent to the operator equations of quantum theory of gravity with canonical rules of quantization of the gravitational and ghost fields. In its operator formulation, the theory can be used to calculate the graviton *S*-matrix as well as to describe the quantum evolution of macroscopic system of gravitons in the non-stationary Universe or in the vicinity of relativistic objects. In the *S*-matrix case, the standard results are obtained. For problems of the second type, the original Heisenberg equations of quantum gravity are converted to a self-consistent system of equations for the metric of the macroscopic space time and Heisenberg operators of quantum fields. It is shown that conditions of the compatibility and internal consistency of this system of equations are performed without restrictions on the amplitude and wavelength of gravitons and ghosts. The status of ghost fields in the various formulations of quantum theory of gravity is discussed.

Cite this paper

G. Vereshkov and L. Marochnik, "Quantum Gravity in Heisenberg Representation and Self-Consistent Theory of Gravitons in Macroscopic Spacetime,"*Journal of Modern Physics*, Vol. 4 No. 2, 2013, pp. 285-297. doi: 10.4236/jmp.2013.42039.

G. Vereshkov and L. Marochnik, "Quantum Gravity in Heisenberg Representation and Self-Consistent Theory of Gravitons in Macroscopic Spacetime,"

References

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[4] S. Perlmutter, et al., “Measurements of Omega and Lambda from 42 High Redshift Supernovae,” Astrophysical Journal, Vol. 517, No. 2, 1999, pp. 565-586. doi:10.1086/307221

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[25] L. R. W. Abramo, R. H. Brandenberger and V. F. Mukhanov, “Energy-Momentum Tensor for Cosmological Perturbations,” Physical Review D, Vol. 56, No. 6, 1997, pp. 3248-3257. doi:10.1103/PhysRevD.56.3248

[1] L. Marochnik, D. Usikov and G. Vereshkov, “Cosmological Acceleration from Virtual Gravitons,” Foundation of Physics, Vol. 38, No. 6, 2008, pp. 546-555. doi:10.1007/s10701-008-9220-6

[2] L. Marochnik, D. Usikov and G. Vereshkov, “Graviton, Ghost and Instanton Condensation on Horizon Scale of the Universe. Dark Energy as Macroscopic Effect of Quantum Gravity,” arXiv: 0811.4484v2 [gr-qc], 2008, pp. 1-93.

[3] A. G. Riese, et al., “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,” Astronomical Journal, Vol. 116, No. 3, 1998, pp. 1009-1038. doi:10.1086/300499

[4] S. Perlmutter, et al., “Measurements of Omega and Lambda from 42 High Redshift Supernovae,” Astrophysical Journal, Vol. 517, No. 2, 1999, pp. 565-586. doi:10.1086/307221

[5] G. T’Hooft and M. Veltman, “One-Loop Divergencies in the Theory of Gravitation,” Annals of Institute Henri Poincare, Vol. 20, No. 1, 1974, pp. 69-94.

[6] M. H. Goroff and A. Sagnotti, “Quantum Gravity at Two Loops,” Physics Letters B, Vol. 160, No. 1-3, 1985, pp. 81-85.

[7] P. A. M. Dirac, “The Theory of Gravitation in Hamiltonian Form,” Proceedings Royal Society, Vol. A246, No. 1246, 1958, pp. 333-343.

[8] P. A. M. Dirac, “Fixation of Coordinates in Hamilton Theory of Gravitation,” Physical Review, Vol. 114, No. 3, 1959, pp. 924-930. doi:10.1103/PhysRev.114.924

[9] R. Arnowitt, S. Deser and C. W. Misner, “Canonical Variables for General Relativity,” Physical Review, Vol. 117, No. 6, 1960, pp. 1595-1602. doi:10.1103/PhysRev.117.1595

[10] L. D. Faddeev, “Hamilton Form of the Theory of Gravity,” Proceedings of the V International Conference on Gravitation and Relativity, Tbilisi, 1968, pp. 54-56.

[11] L. D. Faddeev and V. N. Popov, “Covariant Quantization of the Gravitational Field,” Soviet Physics—Uspekhi, Vol. 16, No. 6, 1974, pp. 777-789. doi:10.1070/PU1974v016n06ABEH004089

[12] N. P. Konopleva, V. N. Popov and N. M. Queen, “Gauge Fields,” Harwood Academic Publishers, Amsterdam, 1981.

[13] R. P. Feymann, “Quantum Theory of Gravittation,” Acta Physics Polonica, Vol. 24, No. 6, 1963, pp. 697-722.

[14] L. D. Faddeev and V. N. Popov, “Feynman Diagrams for the Yang-Mills Field,” Physics Letters B, Vol. 25, No. 1, 1967, pp. 29-30. doi:10.1016/0370-2693(67)90067-6

[15] L. H. Ford and L. Parker, “Quantized Gravitational Wave Perturbations in Robertson-Walker Universes,” Physical Review D, Vol. 16, No. 6, 1977, pp. 1601-1608. doi:10.1103/PhysRevD.16.1601

[16] F. Finelli, G. Marozzi, G. P. Vacca and G. Venturi, “Adiabatic Regularization of the Graviton Stress-Energy Tensor in de Sitter Space-Time,” Physical Review D, Vol. 71, No. 2, 2005, 5 p. doi:10.1103/PhysRevD.71.023522

[17] L. D. Faddeev, “Feynman Integral for Singular Lagrangians,” Theoretical and Mathematical Physics, Vol. 1, No. 1, 1969, pp. 1-13. doi:10.1007/BF01028566

[18] A. B. Borisov and V. I. Ogievetsky, “Theory of Dynamical Affine and Conformal Symmetries as Gravity Theory,” Theoretical and Mathematical Physics, Vol. 21, No. 3, 1975, pp. 1179-1188. doi:10.1007/BF01038096

[19] L. D. Faddeev and A. A. Slavnov, “Gauge Fields. Introduction to Quantum Theory,” 2nd Edition, Addison-Wesley Publishing Company, Boston, 1991.

[20] B. S. DeWitt, “Quantum Theory of Gravity. I. The Canonical Theory,” Physical Review, Vol. 160, No. 5, 1967, pp. 1113-1148.

[21] B. S. DeWitt, “Quantum Theory of Gravity. II. The Manifestly Covariant Theory,” Physical Review, Vol. 162, No. 5, 1967, pp. 1195-1239. doi:10.1103/PhysRev.162.1195

[22] L. H. Ford, “Quantum Instability of De Sitter Space-Time,” Physical Review D, Vol. 31, No. 4, 1985, pp. 710-717. doi:10.1103/PhysRevD.31.710

[23] J. Garriga and T. Tanaka, “Can Infrared Gravitons Screen Lambda?” Physical Review D, Vol. 77, No. 2, 2008, 9 p. doi:10.1103/PhysRevD.77.024021

[24] N. C. Tsamis and R. P. Woodard, “Reply to ‘Can Infrared Gravitons Screen Lambda?’” Physical Review D, Vol. 78, No. 2, 2008, 7 p. doi:10.1103/PhysRevD.78.028501

[25] L. R. W. Abramo, R. H. Brandenberger and V. F. Mukhanov, “Energy-Momentum Tensor for Cosmological Perturbations,” Physical Review D, Vol. 56, No. 6, 1997, pp. 3248-3257. doi:10.1103/PhysRevD.56.3248