n Localization in Brane World

关于“Brane World”的研究，我们主要做了以下两方面的研究：1.为了实现“Brane World”的概念，我们必须证明所有的局域场都局域在三维薄膜上，这就是我们的四维世界。我提出了一种全新的局域化机制，其中只利用了引力相互作用。1984年，Green和Schwarz提出了具有明显时空超对称性的超弦的第一量子化作用，后来将其推广到超膜。但作用量的协变量子化问题在近二十年来一直是一个重要的问题。最近，Berkovits提出了一个有趣的想法，通过使用纯旋量来解决这个问题。我和我的合作者已经澄清了Berkovits方法的一些观点，例如，Green-Schwarz作用量和Berkovits作用量之间的关系，以及纯旋量形式主义从超嵌入形式主义的起源。此外，我们还在纯旋量的基础上构造了超粒子的矩阵模型，并阐明了b-反重影的性质。

Relating to the study of "Brane World", we have mainly performed the following two kinds of research :1. In order to realize an idea of "Brane World", we have to show that all the local fields are localized on the 3-brane, which is regarded as our four dimensional world. I have made a completely new mechanism of the localization where only the gravitational interaction is utilized.2. In 1984, Green and Schwarz have proposed a first-quantized action of superstrings with a manifest space-time supersymmetry, which was extended to supermembranes later. But the problem of the covariant quantization of the action has remained as an important problem for about twenty years. Recently, Berkovits has proposed an interesting idea for solving this problem by using the pure spinor. I and my collaborators have clarified some points of the Berkovits approach, for instance, the relation between the Green-Schwarz action and the Berkovits one, and the origin of the pure spinor formalism from the superembedding formalism. Moreover, we have constructed a matrix model of superparticle based on the pure spinor and clarified the properties of b-antighost.