arXiv 1207.06372012-07-03gr-qcastro-ph.COhep-th

量子引力的新基态

New ground state for quantum gravity

Joao Magueijo, Laura Bethke

摘要：

在本文中，我们推测在量子引力中存在一个新的“基态”，为暴胀宇宙提供了波函数。我们给出了它在联络表象中的显式微扰表达式，并给出了相应的内积。这种状态是手征的，依赖于伊米尔齐参数，是引力子粒子第二量子化理论的真空。我们确定了物理和非物理希尔伯特子空间。然后，我们将这种状态与扰动Kodama状态进行对比，并解释为什么后者永远不能描述引力子在德西特背景。相反，它描述了自对偶激发，这是右手引力子的正频率和左手引力子的负频率的复合物。在我们已经确定的内积下，这些激发被证明是非物理的。我们对儿玉态的拒绝有一个道德故事：量子引力的半经典极限可能是与现实接触的错误路径（现实有时可能是微扰的，但仍然是完全量子的）。我们的结果指向一个非微扰的扩展，我们提出了一些关于这个假设状态的性质的说明。

英文摘要：

In this paper we conjecture the existence of a new "ground" state in quantum gravity, supplying a wave function for the inflationary Universe. We present its explicit perturbative expression in the connection representation, exhibiting the associated inner product. The state is chiral, dependent on the Immirzi parameter, and is the vacuum of a second quantized theory of graviton particles. We identify the physical and unphysical Hilbert sub-spaces. We then contrast this state with the perturbed Kodama state and explain why the latter can never describe gravitons in a de Sitter background. Instead, it describes self-dual excitations, which are composites of the positive frequencies of the right-handed graviton and the negative frequencies of the left-handed graviton. These excitations are shown to be unphysical under the inner product we have identified. Our rejection of the Kodama state has a moral tale to it: the semi-classical limit of quantum gravity can be the wrong path for making contact with reality (which may sometimes be perturbative but nonetheless fully quantum). Our results point towards a non-perturbative extension, and we present some conjectures on the nature of this hypothetical state.

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英文摘要：

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