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： 我们考虑了在最小超空间近似下引力-标量场系统的量子化问题。结果表明，在规范固定的去参数化理论中，其中尺度因子扮演时间的角色时，哈密顿量可以唯一地定义为一个自伴算符的平方根，而不会产生任何排序歧义。此外，当尺度因子趋于零时，哈密顿量退化为零且薛定谔方程变得良好定义。因此，宇宙的初始波函数在希尔伯特空间中可以是任意矢量，这展示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.