Abstract
A canonical time parameter corresponding to the synchronous reference frame is found for an isotropic cosmological model with relativistic gas. Canonical quantization of the model is performed. In the quantum theory, the radius of the Universe is an operator-valued function of time, whose values at different moments of time commute among themselves, and the state of the Universe itself does not change with time. In particular, this means that in experiments in which the radius of the Universe is measured, the presence of singularity is unavoidable within a finite interval of time in the past, and, for closed models, in the future.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 9–14, July, 1990.
The authors thank L. D. Faddeev for his interest to their work, and V. A. Franke for stimulating discussions.
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Gorobei, N.N., Luk'yanenko, A.S. Quantum dynamics of an isotropic cosmological model with relativistic gas. Soviet Physics Journal 33, 557–561 (1990). https://doi.org/10.1007/BF00899101
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DOI: https://doi.org/10.1007/BF00899101