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广义相对论广义相对论在扩展相空间中的量子化

The formulation of General Relativity in extended phase space as a way to its quantization

T. P. Shestakova

备注：
4 pages, talk presented at the XII Marcel Grossmann Meeting, Paris, France, July 2009, an equation corrected
发表信息：
Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity (Paris, France, 2009), eds. by T. Damour, R. T Jantzen and R. Ruffini, World Scientific, Singapore, 2012, P. 1462-1464
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摘要：

我们试图找到一个解释的量子行为的早期宇宙呼吁，作为一项规则，惠勒-德威特量子几何动力学依赖于汉密尔顿制定的广义相对论提出的Arnowitt，Deser和Misner（ADM）。尽管这种方法的基本思想是在大约50年前提出的，但即使是现在，我们也不清楚广义相对论的哈密顿表述是什么。Kiriushcheva和Kuzmin最近的一篇论文[arXiv：0809.0097]给出了它的证据，作者声称ADM的公式和Dirac在1958年的开创性工作中所做的公式是不等价的。如果是这样的话，我们就面临着应该选择什么形式主义的问题。另一个问题是，我们需要一个坚实的过程，在相空间中为所有的引力变量（包括规范变量）构造一个变换生成元。提出了扩展相空间的概念。在分析了这种情况后，我们证明了扩展相空间中的Hamilton公式是Dirac和ADM公式的真正替代，并且可以构造为等价于广义相对论的原始（拉格朗日）公式。扩展相空间中的量子化是直接的，并导致一个新的描述量子宇宙中的一个重要的地方是给规范的自由度。

英文摘要：

Our attempts to find an explanation for quantum behavior of the Early Universe appeal, as a rule, to the Wheeler - DeWitt Quantum Geometrodynamics which relies upon Hamiltonian formulation of General Relativity proposed by Arnowitt, Deser and Misner (ADM). In spite of the fact that the basic ideas of this approach were put forward about fifty years ago, even now we do not have clear understanding what Hamiltonian formulation of General Relativity must be. An evidence for it gives a recent paper by Kiriushcheva and Kuzmin [arXiv:0809.0097], where the authors claim that the formulation by ADM and that by Dirac made in his seminal work of 1958 are not equivalent. If so, we face the question what formalism should be chosen. Another problem is that we need a well-grounded procedure of constructing a generator of transformations in phase space for all gravitational variables including gauge ones. It suggests the notion of extended phase space. After analyzing the situation, we show that Hamiltonian formulation in extended phase space is a real alternative to Dirac and ADM formulations and can be constructed to be equivalent to the original (Lagrangian) formulation of General Relativity. Quantization in extended phase space is straightforward and leads to a new description of quantum Universe in which an essential place is given to gauge degrees of freedom.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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