Exactly Solvable Quantum Field Theory and Elementary Particle Physics

我从一个从事基本粒子物理发展的物理学家的角度，对量子场论中的精确可解模型和多体问题进行了一些研究，这与我在此建议被批准之前提交的研究是一致的。所涉及的主题自然分为两类：1）精确可解模型的理论结构; 2）它们在基本粒子物理中的作用。第一部分包括对热力学Betheanstrike的进一步研究（与T.Oota），Painleve超越与Ising关联函数中角转移矩阵的联系（与K.Ito未发表），Berry相位的计算以及XXZ自旋链中具有变化扭转的弦解的涨落。对于2），我用所谓的one-Plaquette哈密顿量（与Chaudhuri，Ooshita，Koike等人）分析了c=1矩阵模型的非微扰效应和多临界点。我还使用双矩阵模型（与Anazawa，石川一起）计算了与引力耦合的最小模型中的双环振幅。我们将其扩展到N环振幅。这些是我从1990年开始的矩阵模型系列作品的一部分。

I have carried out several researches on exactly solvable models in quantum field theory and many-body problems form the point of view of a physicist being engaged in the development of elementary partcle physics.This conforms to the one submitted before this proposal is granted. The subjects persued naturally fall into the categories 1) theoretical structure of exactly solvable models and 2) ther roles playd in elementary particle physics. The 1) includes the further persuit on thermodynamic Betheansatz (with T.Oota), the connection between the Painleve transcendent and the corner transfer matrix in the Ising correlation funcions (with K.Ito unpublished) and the calculation of Berry phase as well as fluctuations of string solutions in the XXZ spin chain with a varying twist. As for 2), I have done the analysis of the nonperturbative effects and that of the multicritical points of c=1 matrix model, using the so-called one-Plaquette hamiltonian (with Chaudhuri, Ooshita, and Koike.) I have also done the computation of two-loop amplitudes in minimal models coupled to gravity, using the two-matrix model (with Anazawa, Ishikawa.) We are extending this to N-loop amplitudes. These are parts of my series of works on matrix models beginning 1990.