NEW METHOD IN THE STUDY OF RELATIVISTIC BOUND STATES

[I]从QCD直接推导出强子的性质是一个非常困难的问题。最近，哈密顿场论作为一种研究束缚态的新方法，在光锥上量子化引起了越来越大的兴趣。光锥量子化中的真空是非常简单的，因此该理论具有非相对论特征。(1)将Tamm-Dancoff近似应用于光锥量子化的二维QED，研究了两介子和三介子的束缚态。通过利用波函数，我们得到了这些状态的直观图像。我们进一步展示了最简单的真空结构--二维QED的theta真空与规范场的零模之间的关系。(2)利用Bloch-Horowitz有效哈密顿量，我们给出了一个四维标量场论的重整化群变换。我们研究了相结构及其与自发对称性破缺的关系(Harada，Yahiro等)。[II]格点规范理论中的Theta项导致欧几里得时空中的复值Boltzmann权，不能作为概率权。基于不可约特征标的正交性的特征标展开法在研究相结构方面具有很强的作用。拓扑电荷分布可以计算，傅立叶变换得到配分函数(Imachi等人)[III]A.谐振子的路径积分是从鞍点方法精确给出的。量子力学中关于Grassmann流形的半经典近似也得到了精确的结果。B.对规范不变性进行了深入的研究。这将有助于理解夸克禁闭机制(Kashiwa等人)。

[I] It is a very difficult problem to directly derive properties of hadrons from QCD.Recently there has been a growing interest in Hamiltonian field theory quantized on the light cone as a novel way of investigating bound states. The vacuum in light-cone quantization is extremely simple, and thus the theory has non-relativistic features.(1) By applying the Tamm-Dancoff approximation to 2-dimensional QED quantized on the light cone, we investigated the two-and three-meson bound states. We obtained intuitive pictures of these states by exploiting the wave functions. We furthermore showed how the theta vacuum of the 2-dimensional QED, the simplest vacuum structure, is related to the zero mode of the gauge field.(2) We formulated a renormalization group transformation for a 4-dimensional scalar field theory by using the Bloch-Horowitz effective Hamiltonian. We investigated the phase structure and the relation to the spontaneous symmetry breaking (Harada, Yahiro et al).[II] Theta term in lattice gauge theory leads to complex valued Boltzmann weight in Euclidean space time and can not be a probability weight. Character expansion method based on the orthogonal property of irreducible characters plays a powerful role to investigate the phase structure. Topological charge distribution can be evaluated and the Fourier transform leads to the partition function (Imachi et al).[III] A.The path integral for a harmonic oscillator is known to be given exactly from the saddle point method. Semi-classical approximation in quantum mechanics on Grassmann manifolds is shown to lead to an exact results too. B.A deep investigation on the gauge invariance is made. It will be helpful to understand quark confinement mechanism (Kashiwa et al).