Quantum gravity and path integrals
Quantum gravity and path integrals
复制标题
量子引力和路径积分
DOI：
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
S. Hawking
中科院分区：
文献类型：
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作者：
S. Hawking
路径积分法似乎最适合于引力的量子化。人们会认为，路径积分的主要贡献来自于接近背景的度量值，即经典爱因斯坦方程的解。在这些背景度规的作用下，场论中出现了一种新的现象--本征量子熵。这与引力作用的标度行为和引力场的拓扑结构有关。关于背景度量的作用的泰勒级数中的二次项给出了单圈修正。在超对称理论中，四次和二次而不是所谓的对数发散相消，从而得到一个没有正则化的有限的单圈项。从单圈项可以得到背景度规上的有效能量动量张量。在蒸发黑洞的情况下，能量动量张量在未来的地平线上将是规则的。通常的微扰展开对于量子引力是失效的，因为泰勒级数中较高的(相互作用)项不受二次(自由)项的约束。为了克服这一点，我建议人们可以用爱因斯坦方程所有复解的作用的指数和的离散和来代替泰勒莫尔级数中项的路径积分，每个解由其单圈项加权。这种方法似乎将引力真空描绘成一个虚拟的普朗克质量黑洞的海洋。
The path-integral method seems to be the most suitable for the quantization of gravity. One would expect the dominant contribution to the path integral to come from metrics which are near background metrics that are solutions of classical Einstein equations. The action of these background metrics gives rise to a new phenomenon in field theory, intrinsic quantum entropy. This is shown to be related to the scaling behavior of the gravitational action and to the topology of the gravitational field. The quadratic terms in the Taylor series of the action about the background metrics give the one-loop corrections. In a supersymmetric theory the quartic and quadratic but not the so-called logarithmic divergences cancel to give a one-loop term that is finite without regularization. From the one-loop term one can obtain the effective energy-momentum tensor on the background metric. In the case of an evaporating black hole, the energy-momentum tensor will be regular on the future horizon. The usual perturbation expansion breaks down for quantum gravity because the higher (interaction) terms in the Taylor series are not bounded by the quadratic (free) ones. To overcome this I suggest that one might replace the path integrals over the terms in the Taylormore » series by a discrete sum of the exponentials of the actions of all complex solutions of the Einstein equations, each solution being weighted by its one-loop term. This approach seems to give a picture of the gravitational vacuum as a sea of virtual Planck-mass black holes.« less