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arXiv 0902.2829hep-thgr-qcmath-phmath.FAmath.MP
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关于整体一维量子引力中的剩余有效势

On the Residual Effective Potential within Global One-Dimensional Quantum Gravity

Lukasz Andrzej Glinka

摘要:

整体一维量子引力是由量子广义相对论中的整体一维猜想产生的量子引力模型,作者在2010年和2012年首次考虑。在这个模型中,整体维度是嵌入到洛伦兹四维时空中的三维空间的度规的行列式。在2012年,作者已经提出这个模型可以推广到任意Lorentzian D +1维时空,其中D是空间的一个维度,并由此得到高维量子引力的整体一维模型。该模型的纯量子力学部分是量子几何动力学中的最小有效模型,由J.A.惠勒和B.在1960年代,Wheeler和DeWitt提出了一种新的有效势,但它与Wheeler和DeWitt提出的有效势有明显的不同。此外,在我们的模型中,求解量子引力的波泛函是单变量光滑函数,因此,在量子引力的霍金公式中存在的费曼泛函积分的麻烦的数学技术是不存在的,这使得它成为一个数学上一致的量子引力理论。在本文中,我们详细讨论了2010年提出的全球一维模型的某一部分,然后在2012年开发。考虑了有效势的广义泛函展开和残差近似,它们描述了嵌入空间,即三维极大对称Einstein流形,并由此导出了量子引力模型中的Newton-Coulomb型势.此外,方案有关的几个选定的具体形式的有效潜力的建议,作为物理上有趣的和讨论。

英文摘要:

The global one-dimensional quantum gravity is the model of quantum gravity which arises from the global one-dimensionality conjecture within quantum general relativity, first considered by the author in 2010 and then in 2012. In this model the global dimension is a determinant of a metric of three-dimensional space embedded into an enveloping Lorentizan four-dimensional spacetime. In 2012, it has already been presented by the author that this model can be extended to any Lorentzian D + 1-dimensional spacetime, where D is a dimension of space, and resulting in the global one-dimensional model of a higher dimensional quantum gravity. The purely quantum-mechanical part of this model is a minimal effective model within the quantum geometrodynamics, introduced by J.A. Wheeler and B.S. DeWitt in the 1960s, but the effective potential is manifestly different from the one considered by Wheeler & DeWitt. Moreover, in our model the wave functionals solving the quantum gravity are one-variable smooth functions and, therefore, the troublesome mathematical technique of the Feynman functional integration present in the Hawking formulation of quantum gravity, is absent is this model, what makes it a mathematically consistent theory of quantum gravitation. In this paper, we discuss in some detail a certain part of the global one-dimensional model already proposed in 2010, and then developed in 2012. The generalized functional expansion of the effective potential and the residual approximation, which describe the embedded spaces which are maximally symmetric three-dimensional Einstein's manifolds, whose lead to the Newton-Coulomb type potential in the quantum gravity model, are considered. Furthermore, scenarios related to few selected specific forms of the effective potential are suggested as physically interesting and discussed.

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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