Non-Perturbative Structure of Quantum Field Theories Including Quantum Gravity

1较低时空维度中的量子引力为了掌握量子引力的某些方面，我们分析了二维时空中的高阶导数和标量张量模型。利用约束算子的代数，我们导出了WKB波泛函和共形反常。特别是，我们已经展示了一种可能性消失的宇宙常数，而不需要微调。2（超级）弦理论作为量子引力理论通过目前的首席研究员和其他人的早期工作，人们早就知道，共形不变的相对论弦理论自然包含爱因斯坦的广义相对论作为一个低能量极限。尽管近年来有许多重要的工作，然而，没有真实的进展，对几何和非微扰公式的理论已经取得。针对这一情况，我们进行了以下调查。(1)在光锥弦场论框架下的研究;我们有 ...更多信息 光锥作用在有限的一类一般坐标变换下具有对称性。我们还证明了对应于声子场真空期望值变化的弦场的重新定义引起弦耦合常数的连续变化。这使得我们有可能在作用量原理的基础上理解这样一个事实，即只有一个连续可变的常数来表征弦理论。(2)对背景无关表述的初步研究：基于研究（1）的结果，我们提出了一种可能的方法，以一种与背景时空度规无关的方式表述弦场论。此后，其他团体进一步发展了这一建议。(3)研究弦理论的紫外线结构;由于对偶性，弦理论不包含紫外线发散，这可能意味着弦理论中的时空几何概念可能与黎曼几何完全不同。我们提议通过假设时空中的一种新的不确定性原理来解释二元性。我们希望我们的建议可能是有用的线索，我们将继续进一步探索各种新的可能性，以制定弦几何。少

1 Quantum gravity in lower spacetime dimensions For the purpose of grasping some aspects of quantum gravity, we have analyzed higher-derivative and scalar-tensor type models in two-dimensional spacetime. We have derived WKB wave functionals and conformal anomalies using the algebra of constraint operators. In particular, we have exhibited a possibility of vanishing cosmological constant without a need of fine tuning.2 (Super) string theories as a theory of quantum gravity Through earlier works by the present head investigator and others, it has long been known that the conformally invariant relativistic string theories naturally contain Einstein's general relativity as a low energy limit. In spite of many important works in recent yeres, however, no real progress toward geometrical and nonperturbative formulations of the theory have been made. In view of this situation, we have made the following investigations. (1) Studies in the framework of light-cone string field theory; we have sh … More own that the light-cone action has a symmetry under a restricted class of general coordinate transformations. We have also shown that a redefinition of the string field corresponging to the change of the vacuum expectation value of the dilaton field induces a continuous change of the string coupling constant. This made possible to understand, on the basis of an action priciple, the fact that there is only one continuously variable constant which characterizes the string theories. (2) Preliminary studies toward background independent formulation;based on the results of the studies (1), we have proposed a possible way of formulating string field theories in a way which is independent of background spacetime metric. This proposal has since been developed further by other groups. (3) Studies of the ultraviolet structure of string theories; the string theories do not contain ultraviolet divergences because of the duality property, which perhaps implies that the concept of spacetime geometry in string theory may be radically different from the Riemannian geometry. We have proposed to interpret the duality property by assuming a new kind of uncertainty principle in spacetime. With a hope that our proposals may be useful clues, we will continue further to explore various new possibilities toward the formulation of string geometry. Less