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Nonperturbative Study of Quantum Gravity and String Theories

量子引力和弦理论的非微扰研究

基本信息

批准号：
09640349
负责人：
NINOMIYA Masao
金额：
$ 1.41万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640349/
关键词：
string theory string field theory field theory quantum gravity statistical field theory renormalization group 2 dimentional gravity Dirac sea 弦理論ブラックホールの量子論ランダム面ブラックホールの量子群超弦理論弦の第2量子化ボソン場の理論 Dirac sea 負エネルギー状態

项目摘要

The superstring theory is one of the most promising candidates for unified theory of the 4 kind of the fundamental interactions in Nature : strong force, weak force, electromagnetic force and gravitational force. It is one of the most interesting problems to investigate the properties of elementary particles and the birth of the universe by completing the superstring theory. Recently there has been a lot of development to construct it nonperturbatively. Among those a formulation in terms of "D brane" which is solitonic excitation and the duality method become important and then a kind of the master theory called M theory has been intensively investigated.However these nonperturbative string theories do not describe creation and annihilation and thus they have not yet come to 2nd quantized string field theory. Then I have been working, with Professor Holger B.Nielsen, the Niels Bohr Institute, Denmark, on constructing string field theory by using the right- and left- moving modes as constituents. In this approach it becomes apparent that we need a new symmetry analogous to the Bose statistics in bosonic particles. By using this symmetry states are formed. We are now working to derive the scattering amplitudes and check whether the duality holds.During the course of studying our string field theory we found the method how to construct the negative energy sea (Dirac sea) for bosonic particles which enables to treat the bosons similar to fermions when second quantizing. Our theory may give a solution to the long standing problem of negative energy states in bosons in quantum field theory.In quantum gravity we considered the gravity in the 2+εdimensional theory near two dimensions by means of the renormalization group and statistical field theory. By studying short distance behavior in detail we obtained scaling law and critical exponents.

超弦理论是自然界中4种基本相互作用（强相互作用、弱相互作用、电磁力和引力）统一理论的最有希望的候选者之一。通过完善超弦理论来研究基本粒子的性质和宇宙的诞生是人们最感兴趣的问题之一。近年来，非微扰地构造它有了很大的发展。其中，关于孤立子激发的D膜的表述和对偶方法成为重要的研究方向，进而出现了一种称为M理论的主理论，但这些非微扰弦理论并不描述产生和湮灭，因此还没有发展到二次量子化弦场论。后来，我和丹麦尼尔斯·玻尔研究所的霍尔格B.尼尔森教授一起工作，用左右运动模作为组成部分来构建弦场论。在这种方法中，很明显，我们需要一种类似于玻色子中玻色统计的新对称性。通过使用这种对称性，形成了状态。我们现在正致力于推导散射振幅和检验对偶性是否成立。在研究弦场论的过程中，我们找到了如何构造玻色子的负能海（Dirac海）的方法，使玻色子在二次量子化时可以像费米子一样处理。在量子引力中，我们利用重整化群和统计场论讨论了2+ε维理论中的引力，并讨论了2+ε维理论中的引力在二维附近的情况。通过对短程行为的详细研究，得到了标度律和临界指数。