论文标题
量子宇宙学的时间演变
Time Evolution in Quantum Cosmology
论文作者
论文摘要
非线性重力系统（例如宇宙空间时间）中时间演变的量子描述尚不清楚。我们在简化的迷你苏普斯空间设置中显示了该系统的时间演变，只要一个固定路径积分，只要一个固定路径积分不在适当的时间内集成即可。使用该规格固定的作用，我们可以在连贯的或经典状态的基础上构建哈密顿量。我们表明，通过构造，相干状态满足了一般相对性的经典动力学方程。他们不满足哈密顿的约束。结果是，在量子重力中不应满足Wheeler-Dewitt方程。古典状态具有自然的非平凡时间进化，因为它们不是哈密顿量的本征态。不受约束的重力理论的一般特征是对经典宇宙中任何一个符号能量密度的无压暗物质成分的预测，这可能导致新的现象学。
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained using a gauge fixed path integral, as long as one does not integrate over proper time. Using this gauge fixed action we can construct a Hamiltonian in the coherent - or classical - state basis. We show that by construction the coherent states satisfy the classical dynamical equations of General Relativity. They do not satisfy the Hamiltonian constraint. A consequence of this is that the Wheeler-DeWitt equation should not be satisfied in quantum gravity. Classical states have a natural non-trivial time evolution since they are not eigenstates of the Hamiltonian. A general feature of the unconstrained quantum theory of gravity is the prediction of a pressureless dark matter component of either sign energy density in the classical universe which may lead to novel phenomenology.
