标题： 大爆炸局域（BKL）映射是否是量子混合主宇宙的固有特征？ 显示英文标题

标题： Is the BKL map an intrinsic feature of the Quantum Mixmaster Universe?

摘要： 我们通过构建相应的惠勒-德维特方程作为伪黎曼小超空间中的相对论量子理论，研究了量子米克斯马斯特动力学。 通过相对论散射的标准S矩阵，从卡斯纳阶段过渡到下一个阶段的跃迁振幅被建立，并由单壁势介导。 我们提供了Misner原始思想的一种连贯且令人信服的表述，即准经典态可以在宇宙奇点附近任意接近而得以幸存。 通过构造一组完整的态，我们证明了当平均总动量足够高时，准经典BKL映射由产生的跃迁振幅保留到新的态（这与Misner的高占据数完全一致）。 该方案可以自然地迭代到初始奇点而不会发生显著的形状变化。 我们还澄清了态局域化所起的作用，特别是指出当入射态分散时，违反卡斯纳映射的可能性不再可以忽略。 因此，类似卡斯纳的波包可以接近初始奇点。 显示英文摘要

摘要： We study the quantum Mixmaster dynamics by constructing the corresponding Wheeler-DeWitt equation as a relativistic quantum theory in a pseudo-Riemannian Mini-superspace. The transition amplitude from a Kasner regime to the next one is built via the standard S-matrix of a relativistic scattering, and mediated by a single wall potential. We provide a coherent and convincing representation of the original Misner's idea that quasi-classical states can survive arbitrarily close to the cosmological singularity. By constructing a complete set of states, we demonstrate that the quasi-classical BKL map is preserved by the resulting transition amplitude to a new state when their mean total momentum is high enough (exactly coinciding with Misner's high occupation numbers). This scheme is naturally iterated to the initial singularity without appreciable shape changes. We also clarify the role played by the state localization, and, in particular, we outline that when the incoming state is spread, the possibility of violating the Kasner map is no longer negligible. Thus, Kasner-like wave packets can approach the initial singularity.