标题： 经典解的缺失在 Bianchi I 量子宇宙学中的环方法 显示英文标题

标题： Absence of pre-classical solutions in Bianchi I loop quantum cosmology

摘要： 圈量子宇宙学，即为了研究各种宇宙学情况而对量子几何进行对称性约化，导致其量子演化方程的差分方程。 为了确保该方程的解在远离奇点时以预期的经典方式起作用，对解施加了额外的限制。 在本文中，我们考虑了Bianchi I模型，包括真空情况和加入宇宙学常数的情况，并使用生成函数技术证明只有零解满足这些约束。 这意味着要么当前量化演化方程的方法存在技术困难，要么圈量子引力对物理上允许的解施加了严格的限制。 显示英文摘要

摘要： Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this paper, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.