标题： 宇宙的初始波函数是任意的 显示英文标题

标题： Initial wave-function of the universe is arbitrary

摘要： 我们考虑在最小超空间近似下引力-标量场系统的量化。 结果表明，在规范固定去参数化的理论中，尺度因子扮演时间的角色，哈密顿量可以唯一地定义为一个自伴算子的平方根，而没有任何排序歧义。 此外，当尺度因子消失时，哈密顿量退化为零，薛定谔方程变得良好。 因此，宇宙的初始波函数在希尔伯特空间中可以是任意向量，这表明了量子宇宙学中初始条件问题的严重性。 显示英文摘要

摘要： We consider quantization of the gravity-scalar field system in the minisuperspace approximation. It turns out that in the gauge fixed deparametrized theory where the scale factor plays the role of time, the Hamiltonian can be uniquely defined without any ordering ambiguity as the square root of a self-adjoint operator. Moreover, the Hamiltonian degenerates to zero and the Schr\"{o}dinger equation becomes well behaved as the scale factor vanishes. Therefore, there is no technical or physical obstruction for the initial wave-function of the universe to be an arbitrary vector in the Hilbert space, which demonstrates the severeness of the initial condition problem in quantum cosmology.