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Abstract <p>In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture on a nontrivial topology of the Universe which was supported by Wheeler, Hawking, and other founders of quantum gravity. However, this conjecture appears to be in contradiction with the assumption on asymptotic states that is used in the path integral quantization of gauge theories. The presence of asymptotic states ensures gauge invariance of the theory, but, in the case of gravity, these states exist only in asymptotically flat space–times, which restricts possible topologies. Then we have two ways. The first way is to consider only asymptotically flat space–times. In fact, it reduces quantum gravity to quantum field theory in a given background. The second way is to reject the assumption on asymptotic states. In the case of a nontrivial topology, one cannot cover the whole space–time with a single coordinate system. One has to introduce various reference frames fixed by different gauge conditions in different space–time regions. The Hamiltonian describing a gravitating system will depend on gauge conditions. It leads to the conclusion that a unitary evolution may be broken down. This conclusion cannot be obtained in approaches based on the Wheeler–DeWitt equation or making use of the assumption on asymptotic states. The assessment of this conclusion is given.</p>

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Some Features of the Extended Phase Space Approach to Quantization of Gravity#

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • T. P. Shestakova

摘要

Abstract

In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture on a nontrivial topology of the Universe which was supported by Wheeler, Hawking, and other founders of quantum gravity. However, this conjecture appears to be in contradiction with the assumption on asymptotic states that is used in the path integral quantization of gauge theories. The presence of asymptotic states ensures gauge invariance of the theory, but, in the case of gravity, these states exist only in asymptotically flat space–times, which restricts possible topologies. Then we have two ways. The first way is to consider only asymptotically flat space–times. In fact, it reduces quantum gravity to quantum field theory in a given background. The second way is to reject the assumption on asymptotic states. In the case of a nontrivial topology, one cannot cover the whole space–time with a single coordinate system. One has to introduce various reference frames fixed by different gauge conditions in different space–time regions. The Hamiltonian describing a gravitating system will depend on gauge conditions. It leads to the conclusion that a unitary evolution may be broken down. This conclusion cannot be obtained in approaches based on the Wheeler–DeWitt equation or making use of the assumption on asymptotic states. The assessment of this conclusion is given.