Status of physical observables of a friedmann universe in the classical and quantum hamiltonian formalisms |
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Authors: | Yu P Palii V V Papoyan V N Pervushin |
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Institution: | (1) Joint Institute for Nuclear Research, Dubna, Russia, Erevan State University, Armenia |
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Abstract: | The paper is devoted to an investigation of the relationships between the classical Friedmann cosmology and the Dirac Hamiltonian
approach to quantization of the universe, based on the simple but important example of a homogeneous universe filled with
excitations of a scalar field. The method of gaugeless reduction is used to completely separate the sector of physical variables
from the purely gauge sector, making it possible to find the relationship between cosmological observables in the Friedmann
— Einstein sense and observables of the Dirac Hamiltonian formalism in the Narlikar conformai reference frame. Gaugeless reduction
enabled us to establish that in the process of reduction, one of the variables of the nonphysical sector is converted into
an invariant time parameter and cannot be treated as a dynamical variable in either the functional or the operator approach
to quantization. It is shown that in this conversion of a variable into a time parameter, the Hartle-Hawking functional integral
is the reason why the wave function of the Wheeler—De Witt (WDW) equation cannot be normalized and why an infinite gauge factor
arises. The gaugeless reduction provides a certain recipe for mathematical and physical interpretation of the WDW equation
and wave functions, the use of which makes their relationship to observational cosmology clear and transparent. It is shown,
in particular, how the WDW wave function describes the Friedmann evolution with respect to proper time.
Translated from Astrofizika, Vol. 40, No. 2, pp. 303–321, April–June, 1997. |
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