Steepest-descent contours in the path-integral approach to quantum cosmology. I. The de Sitter minisuperspace model.
Steepest-descent contours in the path-integral approach to quantum cosmology. I. The de Sitter minisuperspace model.
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量子宇宙学路径积分方法中的最速下降轮廓。
DOI：
10.1103/physrevd.39.2206
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
J. Louko
中科院分区：
文献类型：
--
作者：
J. Halliwell;J. Louko
我们考虑了一个简单的精确可解模型--De Sitter微超空间模型，在波函数的路径积分表示中寻找收敛的积分轮廓的问题。根据Hartle的建议，我们在复四度规空间中寻找最陡下降的等高线。我们确定了给出Wheeler-DeWitt方程或Wheeler-DeWitt算子的格林函数解的所有可能的等高线。我们尝试应用Hartle和Hawking的边界条件建议。我们发现，该方案并不唯一地固定解，因为尽管路径的起始点是固定的，但轮廓不是唯一的。我们找到了一条表示Vilenkin波函数的等高线，并讨论了Hartle-Hawking波函数和Vilenkin波函数的区别。我们还讨论了在复杂指标上集成的一些含义。一个后果是，即使是在半经典水平上，指标的签名也没有得到尊重。
We consider the issue of finding a convergent contour of integration in the path-integral representation of the wave function for a simple exactly soluble model, the de Sitter minisuperspace model. Following a suggestion of Hartle, we look for the steepest-descent contour in the space of complex four-metrics. We determine all the possible contours which give solutions to the Wheeler-DeWitt equation or Green's functions of the Wheeler-DeWitt operator. We attempt to apply the boundary-condition proposal of Hartle and Hawking. We find that the proposal does not fix the solution uniquely because, although the initial point of the paths is fixed, the contour is not. We find a contour which represents the Vilenkin wave function and discuss the differences between the Hartle-Hawking and Vilenkin wave functions. We also discuss some of the implications of integrating over complex metrics. One consequence is that the signature of the metric is not respected, even at the semiclassical level.