# Quantum geometrodynamics creates new problems

*T.P. Shestakova*^{1}

(1) Department of Theoretical and Computational Physics, Southern Federal University, Sorge St. 5, Rostov-on-Don 344090, Russia

### Abstract

The recent development in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage, the main task was to apply the known quantization schemes to the gravitational field or a certain cosmological model. This trend has led to realization of the fact that a quantum description of the Universe is impossible without implicit or explicit indication to a reference frame represented by some medium filling the whole Universe, with its own equation of state and thermodynamical properties. Thus questions arise: should one seek a "privileged" reference frame or consider the whole variety of gauge conditions and appropriate solutions for the wave function? It is worth noting that the thermodynamic properties of such a quantum Universe would also depend on a chosen reference frame to some extent. So, we need a self-consistent quantum-theoretical and thermodynamic description of the Universe.

### References

- B. S. DeWitt, Phys. Rev. 160, 1113 (1967).
- P. A. M. Dirac, Can. J. Math. 2, 129 (1950).
- P. A. M. Dirac, Proc. Roy. Soc. A 246, 326 (1958).
- R. Arnowitt, S. Deser and C. W. Misner, in: Gravitation, an Introduction to Current Research, ed. by L. Witten (John Wiley & Sons, New York, 1963).
- J. A. Wheeler, in: Relativity, Groups and Topology, ed. by C. DeWitt, B. S. DeWitt (Gordon & Breach, New York, 1964).
- J. A. Wheeler, Einstein's vision (Springer Verlag, Berlin - Heidelberg - New York, 1968).
- C. Isham, Canonical quantum gravity and the problem of time. Lectures presented at NATO Advanced Study Institute, Salamanca, June 1992, Arxiv: gr-qc/9210011.
- S. Mercuri and G. Montani, Int. J. Mod. Phys. D 13, 165 (2004).
- S. Mercuri and G. Montani, in: Proceeding of the X Marcel Grossmann meeting, Rio de Janeiro, Brazil, July 2003, Arxiv: gr-qc/0401127.
- A. O. Barvinsky and V. N. Ponomariov, Izvestiya Vuzov. Fizika, No. 3, 37 (1986).
- J. J. Halliwell, Phys. Rev. D 38, 2468 (1988).
- V. A. Savchenko, T. P. Shestakova and G. M. Vereshkov, Grav. Cosmol. 7, 18 (2001).
- V. A. Savchenko, T. P. Shestakova and G. M. Vereshkov, Grav. Cosmol. 7, 102 (2001).
- J. D. Brown and K. V. Kuchar, Phys. Rev. D 51, 5600 (1995).
- M. V. Battisti and G. Montani, Phys. Lett. B 637, 203 (2006).

For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page