Space-Time Independent Formulation of String Theories

在弦理论的基础上，我们开始了构建包括引力在内的基本粒子基本相互作用统一理论的研究。我们的目标是，特别地，以这样一种方式寻找弦理论的公式，即理论不依赖于特定的背景时空几何。为此目的，我们提出了具体的问题。也就是说，我们澄清了迄今为止尚未触及的弦理论的数学复杂方面，深入了解了早期宇宙的真空结构，并试图将弦对称扩展到非质量壳。让我们回顾一下我们所取得的成就。我们分析了光锥弦场理论中已知的洛伦兹异常的抵消机制。采用s -矩阵方法。路径积分的形式。我们澄清了PHI^3理论在数学上的复杂特征，它已被作为一个几何独立的公式提出。特别地，我们用中点时间规定证明了在一般坐标变换下的不变性。回到爱因斯坦最初的引力理论。我们解决了无隧穿势垒的引力瞬子引起的相变和拓扑变化问题。这项研究预计将有助于仔细研究早期宇宙的真空结构。我们提倡用玻恩-奥本海默方法取代半经典近似。以路径积分法和弦场理论为基础，把握两种方法之间的联系。研究了“弦发射顶点算子”的概念。证明了第一种方法中顶点Weyl不变性的要求与第二种方法中的经典运动方程是等价的。根据路径积分方法中实际的离壳散射振幅，研究了BRST对称性在场论方法中的意义。对二维重力矩阵模型中发现的维拉索罗代数给出了物理解释。我们的解释参考了连续统非临界弦理论。作为我们研究的副产品。本文讨论了二维量子色动力学的代数推广。本文还对光锥规范弦场理论进行了全面的评述。少

We have started our research for constructing the unified theory of fundanmental interactions of elementary particles including gravity on the basis of string theories. Our aim is, in particular, to look for the string theory formulation in such a way that the theory does not depend on a particular background space-time geometry. For this purpose we have set forth with concrete problems. Namely, we clarified mathematically complicated aspects of string theories left untouched so far, gained deep insights into the vacuum structures in the early universe, and tried to extend the stringy symmetries to the off-mass-shell. Let us survey what we have achieved.1. We analyzed the mechanism of cancellation of the Lorentz anomaly known in the light-cone string field theory. By using the methods of S-matrix approach. And of path integral formalism.2. we clarified mathematically complicated features of the PHI^3 theory, which has been put forward as a geometry independent formulation. In particula … More r, we proved the invariance under the general coordinate transformation by using the mid-point time prescription.3. Going back to the original Einstein theory of gravity. We tackled the phase transition problem accompanied by topology change caused by gravitational instantons with no tunneling barrier. This study is expected to serve to scrutinize the vacuum structures in the early universe. We advocated the usefulness of the Born-Oppenheimer method which is supposed to replace the semi-classical approximation .4. To grasp the connection between the two approaches based on the path integral method and the string field theory. We investigated the concept of "string emission vertex operator" . It has been proved that the requirement of the Weyl invariance the vertex in the first approach is equivalent to the classical equation of motion in the latter. The implications of the BRST symmetry in the field theory approach is investigated in terms of the actual off-shell scattering amplitudes in the path integral approach.5. A physical interpretation was given of the Virasoro algebra discovered in the two-dimensional matrix models of gravity. Our interpretation is referred to the continuum non-critical string theory.6. As a byproduct of our research. There is a paper on the algebraic extension of two-dimensional quantum chromodynamics. There is also a comprehensive review article on the light-cone gauge string field theory. Less