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Quantum gravity in 2+epsilon dimensions and renormalization group

2 epsilon 维度的量子引力和重正化群

基本信息

批准号：
06640380
负责人：
KITAZAWA Yoshihisa
金额：
$ 1.34万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1996
项目状态：
已结题

项目摘要

The purpose of this research is to deepen our understanding of quantum gravity by the 2+epsilon demensional expansion method. The quantization of the gravitational interaction is the one of the principle problem in particle physics. The fundamental difficulty of this problem resides in the nonrenormalizability. We can avoid this problem by the 2+epsilon dimensional expansion method near two dimensions. The quantum gravity in 2+epsilon dimension is theoretically interesting due to this reason and may possess qualitatively similar feature with four dimensional qunatum gravity. I have constructed a proof of the renormalizabilty in a formalism which preserves the manifest volume preserving diffeomorphism with my collaborators. In this proof we have used the fact that the structure of the divergences which appear the the perturbative evaluation of the effective action is strongly constrained by the BRS invariance. The conformal invariance is broken by the quantum anomaly near two dimension. However its structure is well understood and the divergences have to be consistent with the anomaly.I have further performed an explicit calculation at the two loop level with my collaborator. We are able to calculate the scaling exponent of the gravitational coupling constant near the untraviolet fixed point of the space time which becomes the scale invariant.We have adopted a manifestly covariant calculation procedure and we are able to estimate a large quntum effect near such a fixed point. We are the first to derive the nontrivial scaling exponent at the fixed point in quantum gravity since thw two loop level calculation is necesarily for this purpose.

本研究的目的是用2+维展开方法加深我们对量子引力的理解。引力相互作用的量子化是粒子物理学的基本问题之一。这个问题的根本困难在于不可重正化性。我们可以避免这个问题，通过2+ 10维展开方法接近二维。由于这个原因，2+ 1维的量子引力在理论上是有趣的，并且可能具有与四维量子引力定性相似的特征。我构造了一个证明的renormalizabilty在形式主义，保持显体积保持同形与我的合作者。在这个证明中，我们使用了这样一个事实，即出现在有效作用量的微扰评估中的发散的结构受到BRS不变性的强烈约束。二维附近的量子反常破坏了共形不变性。然而，它的结构是很好的理解和分歧必须与异常一致。我进一步执行了显式计算，在两个循环的水平与我的合作者。我们能够计算出时空非紫外不动点附近引力耦合常数的标度指数，该不动点成为标度不变量，我们采用了显协变的计算方法，并且能够估计出在这样的不动点附近的大量子效应。本文首次导出了量子引力中不动点处的非平凡标度指数，因为两圈能级计算是为此目的而进行的。