arXiv 1206.08302012-06-05gr-qchep-th

将时间依赖性恢复到量子宇宙学中

Restoring Time Dependence into Quantum Cosmology

Aharon Davidson, Ben Yellin

备注：: Honorable Mentioned essay - Gravity Research Foundation 2012
发表信息：: IJMPD 21, 1242011 (2012)
DOI：: 10.1142/S0218271812420114

摘要：

迷你超空间宇宙学将比例因子$a(t)$、时滞函数$n(t)$和可选的膨胀场$ϕ(t)$视为正则变量。虽然预先固定$n(t)$意味着失去哈密顿约束，但在此级别上预先固定$a(t)$偶然是无害的。这表明了哈特-霍金方法的替代方案，其中预先固定的$a(t)$及其导数被视为时间的显式函数，留下$n(t)$和现在强制的$ϕ(t)$作为规范变量。朴素规范前缀$a(t)=const$显然是被禁止的，这会导致演化完全冻结，因此，预先固定标度因子，比如说$a(t)=t$，必然会在拉格朗日量中引入显式的时间依赖性。利用Dirac处理约束的方法，构造了相应的超时空微哈密顿量，并计算了Dirac括号，用$\{n,ϕ\}_D\neq 0$刻画，推广到量子理论中的对易关系.

英文摘要：

Mini superspace cosmology treats the scale factor $a(t)$, the lapse function $n(t)$, and an optional dilation field $ϕ(t)$ as canonical variables. While pre-fixing $n(t)$ means losing the Hamiltonian constraint, pre-fixing $a(t)$ is serendipitously harmless at this level. This suggests an alternative to the Hartle-Hawking approach, where the pre-fixed $a(t)$ and its derivatives are treated as explicit functions of time, leaving $n(t)$ and a now mandatory $ϕ(t)$ to serve as canonical variables. The naive gauge pre-fix $a(t)=const$ is clearly forbidden, causing evolution to freeze altogether, so pre-fixing the scale factor, say $a(t)=t$, necessarily introduces explicit time dependence into the Lagrangian. Invoking Dirac's prescription for dealing with constraints, we construct the corresponding mini superspace time dependent total Hamiltonian, and calculate the Dirac brackets, characterized by $\{n,ϕ\}_D\neq 0$, which are promoted to commutation relations in the quantum theory.

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