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arXiv 2007.05875gr-qchep-thmath-phmath.MP
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超局域经典和量子引力理论

An Ultralocal Classical and Quantum Gravity Theory

John R. Klauder

摘要:

任何经典场论的超局部形式消除了其作用泛函中的所有空间导数,例如,哈密顿函数密度它已被应用于协变标量场理论,甚至被皮拉蒂应用于爱因斯坦的广义相对论,作为微扰级数的初始项,旨在恢复所有遗漏的导数。在此之前,作者已经通过仿射量子化超局域标量场,以表明这些非重正化理论可以正确地通过仿射量子化,这样的标量模型的故事在本文中进行了讨论。本文还将说明超局域引力可以成功地用仿射量子化。本研究的目的是,一个成功的仿射量子化的任何超局域场的问题意味着,与适当恢复的衍生物,经典理论,在原则上,可以保证一个成功的结果,使用正则量子化或仿射量子化。特别是,爱因斯坦的引力需要仿射量子化,它将是成功的。

英文摘要:

An ultralocal form of any classical field theory eliminates all spatial derivatives in its action functional, e.g., in its Hamiltonian functional density. It has been applied to covariant scalar field theories and even to Einstein's general relativity, by Pilati, as an initial term in a perturbation series that aimed to restore all omitted derivatives. Previously, the author has quantized ultralocal scalar fields by affine quantization to show that these non-renormalizanle theories can be correctly quantized by affine quantization; the story of such scalar models is discussed in this paper. The present paper will also show that ultralocal gravity can be successfully quantized by affine quantization. The purpose of this study is that a successful affine quantization of any ultralocal field problem implies that, with properly restored derivatives, the classical theory can, in principle, be guaranteed a successful result using either a canonical quantization or an affine quantization. In particular, Einstein's gravity requires an affine quantization, and it will be successful.

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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