Abstract
In Chapter 7 we discussed some specific applications of Einstein’s general relativity and also the general way of formulating the problem of classical geometrodynamics. In the present chapter we shall first examine how quantum geometrodynamics can be formulated with the help of Feynman’s path integral formalism. The sketchy survey of other approaches to quantum gravity in the previous chapter will have convinced the reader that the problem is not simple, whatever means we may choose to adopt for its solution. We begin, therefore, by looking at the difficulties facing the path integral formalism.
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Notes and References
For the discussion of S GH see: Gibbons, G. W., and Hawking, S. W.: 1977, Phys. Rev. D15, 2738.
Hawking, S. W.: 1979, in General Relativity — An Einstein Centenary Survey (eds S. W. Hawking and W. Israel), Cambridge.
For the discussion of the boundary value problem in geometrodynamics, see: Isenberg J., and Wheeler, J. A.: 1979 in Relativity, Quanta and Cosmology (eds M. Pantaleo and F. De Finis), Johnson, New York, p. 267.
A discussion of Green’s functions and their inverses will be found in: Morse, P. M., and Feschbach, H.: 1953, Methods of Mathematical physics, McGraw-Hill, New York.
DeWitt, B. S., and Brehme, R. W.: 1960, Ann. Phys. 9, 220.
The idea of transforming away the spacetime singularity through conformal transformations is discussed in different contexts by: Beem, J. K.: 1976, Commun. Math. Phys. 49, 179.
Kembhavi, A. K.: 1978, Monthly Notices Roy Astron Soc. 185, 807.
The conformal flatness of Robertson-Walker models was first demonstrated by: Infeld, L., and Schild, A.: 1945, Phys. Rev. 68, 250.
The instability of flat spacetime to conformal fluctuations has been discussed by: Atkatz, D., and Pagels, H.: 1982, Phys. Rev. D25, 2065.
Brout, R., Englert, F., Frere, J. M., Gunzig, E., Naradone, P., and Truffin, C.: 1980, Nucl. Phys. B170, 228.
Lindley, D.: 1981, Nature 291, 392.
Padmanabhan, T.: 1983, Phys. Lett. 93A, 116.
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© 1986 D. Reidel Publishing Company, Dordrecht, Holland
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Narlikar, J.V., Padmanabhan, T. (1986). Quantum Conformal Fluctuations. In: Gravity, Gauge Theories and Quantum Cosmology. Fundamental Theories of Physics, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4508-1_12
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DOI: https://doi.org/10.1007/978-94-009-4508-1_12
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