论文标题
纯连接一般相对论的量子宇宙学
Quantum cosmology of pure connection general relativity
论文作者
论文摘要
我们研究了基于（复杂的）连接而不是时空度量的宇宙常数的一般相对论的均匀宇宙学模型，尤其是在一阶理论中，通过在手性平均表格中整合自偶会的两种形式而获得的一阶理论。 Bianchi IX模型的古典动力学在拉格朗日和哈密顿形式主义中进行了研究，我们强调获得真正的洛伦兹解决方案所需的现实条件。这些现实条件的解决方案属于不同的分支，进而导致不同的哈密顿理论，其中只有一种是通常的洛伦兹·比安奇（Lorentzian Bianchi IX）模型。我们还展示了平坦的Bianchi I模型的简单情况，为此，现实条件和动态方程式都大大简化了。我们讨论了真正的欧几里得版本相同理论与这一复杂理论的关系。最后，我们研究了均质和各向同性模型的量子理论，为此，一般相对论的纯连接作用将其降低至纯边界项，并立即评估路径积分，从而重现量子宇宙学的已知结果。这些理论的一个有趣的方面是，有效时空度量的标志，因此对宇宙常数的解释是本质上模棱两可的。
We study homogeneous cosmological models in formulations of general relativity with cosmological constant based on a (complexified) connection rather than a spacetime metric, in particular in a first order theory obtained by integrating out the self-dual two-forms in the chiral Plebanski formulation. Classical dynamics for the Bianchi IX model are studied in the Lagrangian and Hamiltonian formalism, where we emphasise the reality conditions needed to obtain real Lorentzian solutions. The solutions to these reality conditions fall into different branches, which in turn lead to different real Hamiltonian theories, only one of which is the usual Lorentzian Bianchi IX model. We also show the simpler case of the flat Bianchi I model, for which both the reality conditions and dynamical equations simplify considerably. We discuss the relation of a real Euclidean version of the same theory to this complex theory. Finally, we study the quantum theory of homogeneous and isotropic models, for which the pure connection action for general relativity reduces to a pure boundary term and the path integral is evaluated immediately, reproducing known results in quantum cosmology. An intriguing aspect of these theories is that the signature of the effective spacetime metric, and hence the interpretation of the cosmological constant, are intrinsically ambiguous.
