Unitarity approach to quantum cosmology
Unitarity approach to quantum cosmology
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DOI：
10.1016/0370-1573(93)90032-9
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发表时间：
1993-08
期刊：
影响因子：
--
通讯作者：
A. Barvinsky
中科院分区：
文献类型：
--
作者：
A. Barvinsky
本文综述了现代量子宇宙学--空间封闭世界的量子引力理论中的么正性问题。基于真实物理变量通常的路径积分量子化，我们得到了量子宇宙学的标准狄拉克-惠勒-德威特公式，现在它补充了守恒概率幅的算法，从而构成了一个明显的幺正场论。详细讨论了量子宇宙学中多指时间参数化幺正演化的相关问题。我们也给出了Batalin，Fradkin和Vilkovisky（BFV）的相对论规范中的广义正则量子化的评论，并表明Dirac-Wheeler-DeWitt形式主义占据了物理变量量子化和BFV理论之间的中间位置。幺正性方法，这是在形式路径积分量子化的框架内的精确理论中发展起来的，在严格的操作水平上在半经典循环展开的单循环近似中得到了证实。特别是，一般的惠勒-德威特方程的半经典解，并考虑其在早期暴胀宇宙理论的影响。最后简要讨论了三阶量子化的前景以及酉量子宇宙学与欧几里德量子引力的统一。
A review is presented of the unitarity problem in modern quantum cosmology - quantum gravity theory of spatially closed worlds. Based on the usual path-integral quantization of true physical variables, we arrive at the standard Dirac-Wheeler-DeWitt formulation of quantum cosmology, which now becomes supplemented with the algorithms for conserved probability amplitudes and thus constitutes a manifestly unitary field theory. The related issue of the many-fingered time parametrizing the unitary evolution in quantum cosmology is discussed in much detail. We also give a review of the generalized canonical quantization in relativistic gauges of Batalin, Fradkin and Vilkovisky (BFV) and show that the Dirac-Wheeler-DeWitt formalism occupies an intermediate position between quantizing the physical variables and the BFV theory. The unitarity approach, which is developed in the exact theory within the framework of the formal path-integral quantization, is confirmed at a strictly operatorial level in the one-loop approximation of a semiclassical loop expansion. In particular, the general semiclassical solution of the Wheeler-DeWitt equations is presented and its implications in the theory of the early inflationary Universe are considered. The prospects of the third-order quantization and the unification of unitary quantum cosmology with the Euclidean quantum gravity are briefly discussed.