将ADM计算推广到量子场论
Generalizing the ADM Computation to Quantum Field Theory
摘要：
缺乏可识别的低能量子引力效应要求某种渐近级数展开非常精确，但正确的展开可能涉及牛顿常数的平方或分数幂。这就解释了为什么传统的微扰理论显示出无法控制的紫外线发散。我们探讨这种可能性的上下文中的质量的带电，引力标量。这个系统的经典极限在1960年由Arnowitt，Deser和Misner精确地解决了，他们的解决方案确实表现出对牛顿常数的非解析依赖性。我们推导出量子场论系统质量的精确泛函积分表示，然后基于稳相方法的正确实现，为它发展了一种替代的展开式。新的扩展需要在每一阶中添加无限类的新图，并从高阶中减去它们。新展开的零阶项具有第一量子化Klein-Gordon标量的物理解释，该标量在由其自身概率流产生的引力势和电磁势中形成束缚态。我们表明，这种束缚态的存在，我们得到了它们的质量的数值结果。
英文摘要：
The absence of recognizable, low energy quantum gravitational effects requires that some asymptotic series expansion be wonderfully accurate, but the correct expansion might involve logarithms or fractional powers of Newton's constant. That would explain why conventional perturbation theory shows uncontrollable ultraviolet divergences. We explore this possibility in the context of the mass of a charged, gravitating scalar. The classical limit of this system was solved exactly in 1960 by Arnowitt, Deser and Misner, and their solution does exhibit nonanalytic dependence on Newton's constant. We derive an exact functional integral representation for the mass of the quantum field theoretic system, and then develop an alternate expansion for it based on a correct implementation of the method of stationary phase. The new expansion entails adding an infinite class of new diagrams to each order and subtracting them from higher orders. The zeroth order term of the new expansion has the physical interpretation of a first quantized Klein-Gordon scalar which forms a bound state in the gravitational and electromagnetic potentials sourced by its own probability current. We show that such bound states exist and we obtain numerical results for their masses.
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