Quantum Theory of Extended Objects and Unification Theory

点击翻译按钮获取中文摘要

The purpose of this research project was to study the quantum theory of extended objects as candidates for the unified theory. We focused on constructing a quantized theory of membranes and at the same time on deeper understanding of string models. We carried out both I) analysis of the mathematical properties of membranes and II) analysis of their physical properties such as the mass spectrum and quantum effects.I) In constructing quantum theory of membranes it is crucial to understand the gauge symmetries of the model. It has been known that the area preserving diffeomorphisms arises as the residual gauge invariance. This type of diffeomorphisms has recently been shown to be expressed in terms of an infinite dimensional algebra called W_* algebra (n->* limit of W_n algebra). Towards the supersymmetric extension of W_* algebra we have obtained the following results :a) Construction of Supersymmetric Generalization of W Algebrasb) Construction of Supersymmetric Integrable Systems Associated with Super W Algebrasc) Derivation of Super KP Hierarchy Based on Lie Superalgebrasd) The Results a) -c) were Generalized to the N=2 Symmetry Case.These results not only provide useful methods for analyzing supermembranes but also give a useful framework to deal with compactification of superstrings.II) Weyl invariance Plays a crucial role in quantum theory of strings. We have constructed a membrane model with Weyl invariance. We are now in the course of studying quantum effects in this theory. The result of this investigation is expected to have implications on three-dimensional gravity as wel.