关于宇宙学中一个特殊零模算子的泛函行列式
On the functional determinant of a special operator with a zero mode in cosmology
摘要：
用Faddeev-Popov规范固定方法计算了一个特殊的二阶量子力学算符的泛函行列式，并给出了零模的规范固定.这个算子受周期性边界条件的影响出现在早期宇宙理论的应用中，特别是确定了由共形场论（CFT）产生的量子宇宙学中的单圈统计和。计算是针对该算子的周期零模在周期范围内具有两个根（节点）的特殊情况进行的，这对应于CFT驱动宇宙学中的宇宙瞬子类，其欧几里德Friedmann-Robertson-Walker度规的宇宙标度因子具有一个振荡。
英文摘要：
The functional determinant of a special second order quantum-mechanical operator is calculated with its zero mode gauged out by the method of the Faddeev-Popov gauge fixing procedure. This operator subject to periodic boundary conditions arises in applications of the early Universe theory and, in particular, determines the one-loop statistical sum in quantum cosmology generated by a conformal field theory (CFT). The calculation is done for a special case of a periodic zero mode of this operator having two roots (nodes) within the period range, which corresponds to the class of cosmological instantons in the CFT driven cosmology with one oscillation of the cosmological scale factor of its Euclidean Friedmann-Robertson-Walker metric.
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