标题： 各向同性圈量子宇宙学与物质 II：洛伦兹约束 显示英文标题

标题： Isotropic Loop Quantum Cosmology with Matter II: The Lorentzian Constraint

摘要： 洛伦兹哈密顿约束在与无质量标量场耦合的各向同性环量子宇宙学中得到解决。 如同欧几里得情况一样，量子几何的离散性消除了量子弗里德曼模型中的经典奇点。 尽管没有经典奇点，但修改后的德维特初始条件与晚期的平滑行为不相容。 此外，只有在正时间或负时间时才能恢复平滑行为，而不能同时在两者上。 一个重要的特征，与欧几里得情况相同，是系统要动态演化需要一个大约为普朗克能量的最小初始能量。 通过形成物质场的波包，可以得到以内部时间为基准的显式演化。 显示英文摘要

摘要： The Lorentzian Hamiltonian constraint is solved for isotropic loop quantum cosmology coupled to a massless scalar field. As in the Euclidean case, the discreteness of quantum geometry removes the classical singularity from the quantum Friedmann models. In spite of the absence of the classical singularity, a modified DeWitt initial condition is incompatible with a late-time smooth behavior. Further, the smooth behavior is recovered only for positive or negatives times but not both. An important feature, which is shared with the Euclidean case, is a minimal initial energy of the order of the Planck energy required for the system to evolve dynamically. By forming wave packets of the matter field an explicit evolution in terms of an internal time is obtained.