Abstract
The ultralocal representation of the canonically quantized gravitational field is used to obtain the evolution of coherent states in the immediate neighborhood of the singularity. It is shown that smearing functions play the role of classical fields since they correspond to cosmological solutions around the singularity. A special class of ultralocal coherent states is shown to contain the essential aspects of the dynamics of the system when we choose a simple representation for the field operators of the theory. When the ultralocality condition is broken a conjecture will be made about the quantum evolution of coherent states in the classical limit.
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References
Lifshitz, E. M., and Khalatnikov, I. M. (1963).Adv. Phys.,12, 185.
Belinskii, V. A., Khalatnikov, I. M., and Lifshitz, E. M. (1970).Adv. Phys.,19, 525.
Belinskii, V. A., Khalatnikov, I. M., and Lifshitz, E. M. (1982).Adv. Phys.,31, 639.
Eardley, D., Liang, E., and Sachs, R. (1972).J. Math. Phys.,13, 99.
Liang, E. (1972).Phys. Rev. D,5, 2458.
Klauder, J. (1971).Acta Phys. Austr. Suppl. VIII, 227; (1973). Functional Techniques and their Applications, Lectures in Theoretical Physics, W. E. Brittin, ed. (Colorado University Press, Boulder).
Dirac, P. A. M. (1958).Proc. R. Soc. London Ser. A,246, 333.
Arnowitt, R., Deser, S., and Misner, C. (1962). inGravitation, An Introduction to Current Research, L. Witten. ed. (Wiley, New York).
Wheeler, J. A. (1964). inRelativity Groups and Topology, B. S. De Witt, ed. (Gordon and Breach, New York).
De Witt, B. S. (1967).Phys. Rev.,160, 1964.
Isham, C. J. (1976).Proc. R. Soc. London Ser. A,351, 209.
Klauder, J., in Relativity, M. Carmeli, S. Fickler, and L. Witten, ed. (Plenum Press, New York, 1970).
Teitelboim, C. (1973).Ann. Phys. (New York),79, 542.
Hojman, S. A., Kuchar, K., and Teitèlboim, C. (1976).Ann. Phys. (New York),96, 88.
Kuchar, K., inRelativity, Astrophysics and Cosmology, W. Israel, ed. (D. Reidel, Dordrecht, 1973).
Baierlein, R., Sharp, D., and Wheeler, J. (1962).Phys. Rev.,126, 1864; York, J. (1972).Phys. Rev. Lett.,28, 1082.
Landau, L. D., and Lifshitz, E. M.,The Classical Theory of Fields (Pergamon Press, Oxford, 1975).
Misner, C. (1969).Phys. Rev.,186, 1319.
Misner, C., inMagic Without Magic, J. Klauder, ed. (Freeman San Francisco, 1972).
Pilati, M. (1983).Phys. Rev. D,28, 729.
Francisco, G., and Pilati, M. (1985).Phys. Rev. D,31, 241.
Stueckelberg, E. C. G. (1941).Helv. Phys. Acta.,14, 23, 322, 588.
Feynman, R. P. (1950).Phys. Rev.,80, 440.
Horwitz, L. P., and Rorhlich, F. (1981).Phys. Rev. D,24, 1528; Horwitz, L. P., and Lavil, Y. (1982).Phys. Rev. D,26, 819.
Henneaux, M, and Teitelboim, C. (1982).Ann. Phys.,143, 127; Teitelboim, C. (1982).Phys. Rev. D,25, 3159.
Klauder, J., inPath. Integrals and Their Applications, C. J. Papadopoulos and J. T. Devresee, eds. (Plenum Press, New York, 1978).
Hepp, K. (1974).Commun. Math. Phys.,35, 265.
Isham, C. J., and Kakas, A., A group theoretic approach to the canonical quantization of gravity, Imperial College preprint 83-84/44.
Francisco, G. (1984).Classical and Quantum Gravity,1, 621.
Ryan, M., and Shepley, L.,Homogeneous Relativistic Cosmologies (Princeton University Press, Princeton, New Jersey, 1975).
Barrow, J. (1982).Phys. Rep.,85, 1.
Francisco, G., Ph.D. thesis, Imperial College, London (January 84).
Ryan, M.,Hamiltonian Cosmology (Springer-Verlag, Berlin, 1972).
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Francisco, G. The behavior of the gravitational field near the initial singularity. Gen Relat Gravit 18, 287–308 (1986). https://doi.org/10.1007/BF00765888
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DOI: https://doi.org/10.1007/BF00765888