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内容提要:
Mathematics is a rapidly developing field where ideas and methods from many different subjects are interchanged and applied abundantly. One example is String Theory, which has raised many mathematical questions and has motivated the development of surprising new mathematical theories. String Theory has helped to solve many long-standing problems in mathematics, particularly in algebraic geometry. ...
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ALM
The launch of this Advanced Lectures in Mathematics series is amied at keeping mathematicians informed of the latest developments in mathematics,as well as to aid in the learning of new mathematical topics by students all over the world.Each volume consists of either an expository monograph or a collection of significant introductions to important topics.This serise emphasizes the history and sources of motivation for the topics under discussion,and also gives an overview of the current status of research in each particular field.These volumes are the first source to which pepole will turn in order to learn new subjects and to discover the latest results of many cutting-edge fields in mathematics. 目录:
Preface Stephen Hawking: Brane New World Edward Witten: Gauge Theory and Gravity Edward Witten: Easing Into QFT Andrew Strominger: Open String Creation by S-brane Sergio Ferrara: Duality, Gauging and SuperHiggs Effect in String and M-theory Tohru Eguchi, Kazuhiro Sakai: Seiberg Witten Curve for the E-String Theory Louise Dolan, Chiara R. Nappi: Strings and Noncommutativity Eric D'Hoker, D.H. Phong: Lectures on Two-loop Superstrings Eric D'Hoker, I. Krichever and D.H. Phong: Seiberg-Witten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons Zhi-zhong Xing: Quark Mass Hierarchy and Flavor Mixing in Orbifold Models S. Gukov: M-theory on Manifolds with Exceptional Holonomy R. P. Thomas: Stability Conditions and the Braid Group Rong-Gen Cai: Some Remarks on Constant Curvature Spaces Shinobu Hosono: Fourier-Mukai Partners and Mirror Symmetry of K3 Surfaces Shinobu Hosono: Counting BPS States via Holomorphic Anomaly Equations Yi-hong Gao: Symmetries, Matrices, and de Sitter Gravity Miao Li: Correspondence Principle in a PP-wave Background Bin Wang: Support of dS/CFT Correspondence from Spacetime Perturbations 前言:
In celebration of the opening of the Center of Mathematical Sciences at Zhejiang University, we held the 2002 String Theory International Conference from August 12th to August 15th at the new Center. The attendance of more than ten prominent mathematicians such as S.Hawking, D.Gross, and E.Witten was a huge sensation in China. These eminent mathematicians, in addition to S.-T. Yau and A. Strominger, had the honor of meeting the former President Jiang Zemin previously in Beijing. .
The topic of this conference, string theory, has been a burn..
书摘:
Remarkably enough, in many of the theories in the M-theory network, spacetime has more than the four dimensions we experience. Are these extra dimensions real? I must admit I have been reluctant to believe in extra dimensions, but the M-theory network fits together so beautifully, and has so many unexpected correspondences, that I feel to ignore it would be like claiming that God put fossils in the rocks to trick Darwin into believing in evolution.
In some theories in the network, spacetime has ten dimensions, while in others, it has eleven. This is yet another indication of the fact that spacetime and its dimension are not absolute, theory-independent quantities, but derived concepts that depend on the particular mathematical model. So how is it that spacetime appears four-dimensional to us, but is ten or eleven dimensional in M-theory? Why don't we observe another six or seven dimensions? The conventional answer to this question, which was generally accepted until recently, was that the extra dimensions were all curled up in a space of small size, leaving four dimensions that are nearly flat. It is like a human hair: if you look at it from a distance, it looks like a one dimensional line, but if you look at it under a magnifying glass, you see the thickness and that the hair is really three-dimensional. In the case of spacetime, a sufficiently powerful magnifying should reveal curled-up extra dimensions, if they exist. In fact, we can probe spacetime to short distances using high energy particles produced by big particle accelerators like the large hadron collider being built in Geneva. So far at least, we have not detected evidence for dimensions beyond four. If this picture is correct, the extra dimensions would have to be curled up smaller than a billion-billionth of a centimeter. |