Japan JSPS Program: Quantum Integrability and Strong-Weak Coupling Quality of the Affine Toda Field Theories

该奖项为日本京都汤川理论物理研究所的Andrew J. Bordner博士提供为期12个月的日本科学促进会（JSPS）博士后奖学金。Bordner博士将与Ryu Sasaki教授一起进行一项名为“仿射- Toda场论的量子可积性和强弱耦合对偶性”的研究项目。提出的研究将检验量子场论中所涉及的等效性，该理论显示了基本粒子之间强相互作用的特征，同时也表明了弱相互作用。这个等价对于理解如何在强耦合理论中计算物理量是有用的，例如描述核力的理论。拟议的研究将检验一类特殊的理论，称为“仿射- toda场”，其基本原理是假设它们不仅表现出强-弱耦合等价，而且假设它们允许在没有任何初始近似方法的情况下计算所有物理量。过去，物理量只能在弱耦合的理论中计算，并且只能使用近似方法。这种可解性导致了s矩阵的假设形式，s矩阵是一个描述由于耦合而产生的任意数量粒子散射的概念。这项研究将为不同的量子场理论实际上是同一理论的不同表述提供一个有价值的测试，这一发现可能最终为如何从夸克的基本理论预测核子的性质提供一个解决方案。＊＊＊

Bordner 9703595 This award supports a 12 month Japan Society for the Promotion of Science (JSPS) Postdoctoral Fellowship for Dr. Andrew J. Bordner at the Yukawa Institute for Theoretical Physics, Kyoto, Japan. Dr. Bordner will work with Dr. Ryu Sasaki, professor, on a research project entitled, "Quantum Integrability and Strong-Weak Coupling Duality of the Affine- Toda Field Theories." The proposed research will examine the equivalence involved in a quantum field theory that displays characteristics of strong interactions between fundamental particles, yet, at the same time, indicates weak mutual interactions. This equivalence would be useful in understanding how to calculate physical quantities in a strongly coupled theory, such as that describing nuclear forces. The proposed research will examine a particular class of theories designated "Affine-Toda field", the rationale being that they are hypothesized to exhibit not only strong-weak coupling equivalence, but are also hypothesized to allow the calculation of all physical quantities without any initial approximation methods. In the past, physical quantities have been calculated only in theories with a weak coupling, and then only using approximation methods. This solvability has led to a postulated form for the S-matrix, a concept that describes the scattering of an arbitrary number of particles as a result of coupling. The research will provide a valuable test of how different quantum field theories are in fact different formulations of the same theory, a finding that may eventually provide a solution for how to predict properties of nucleons from a fundamental theory of quarks. ***