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arXiv 1507.01149gr-qchep-th
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耦合于标量场的圈量子引力

Loop quantum gravity coupled to a scalar field

Jerzy Lewandowski, Hanno Sahlmann

摘要:

我们重新考虑耦合到克莱因-戈登时间场的引力的Rovelli-Smolin模型,着眼于捕获在时间被标量场去参数化的框架中丢失的标量场的自由度。得到了圈量子引力的几个新结果:(i)构造了引力-物质系统的Hilbert空间及其上标量场的非标准表示;(ii)定义并研究了耦合系统标量约束的新算符;(iii)发展了求解约束的方法.新约束的交换子不会消失,但似乎再现了狄拉克代数的一部分。然而,这给寻找解决办法带来了问题。因此,我们考虑的状态--也许是整个设置--仍然需要一些改进。作为一个侧面的结果,我们描述了一个表示的重力自由度,其中通量是对角线。这种表示与Dittrich和Geiller的BF真空非常相似。

英文摘要:

We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field. Several new results for loop quantum gravity are obtained: (i) a Hilbert space for the gravity-matter system and a non-standard representation of the scalar field thereon is constructed, (ii) a new operator for the scalar constraint of the coupled system is defined and investigated, (iii) methods for solving the constraint are developed. Commutators of the new constraint do not vanish, but seem to reproduce a part of the Dirac algebra. This, however, poses problems for finding solutions. Hence the states we consider -- and perhaps the whole setup -- still needs some improvement. As a side result we describe a representation of the gravitational degrees of freedom in which the flux is diagonal. This representation bears a strong resemblance to the BF vacuum of Dittrich and Geiller.

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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