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Numerical and analytical investigations of the lattice gauge models at finite temperatures by renormalization group approach

通过重正化群方法对有限温度下的晶格规范模型进行数值和分析研究

基本信息

批准号：
60540185
负责人：
IMACHI Masahiro
金额：
$ 0.64万
依托单位：
Department of Physics, Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1985
资助国家：
日本
起止时间：
1985 至 1986
项目状态：
已结题

项目摘要

1. The lattice gauge theory (LGT) at finite temperatures is investigated in the Migdal renormalization group (RG) approach. Starting from various bare theories defined by various bare coupling constants, we arrive at a unique renormalized theory after sufficient number of Migdal RG transformations. This behavior is seen with a set of infinite number of coupling constants corresponding to the infinite number of irreducible representations. Each action is represented by a point in the infinite dimenensional coupling constant space. RG transformations drive the point to a unique renormalized trajectory independent of the bare action. Migdal RG transformation at T=0 is expressed by isotropic scale transformations. To investigate T<>0 systems, asymmetric scale transformation where the scale in timelike direction is fixed is necessary. We investigated SU(2) and SU(3) LGT's at T<>0. RG flow at T<>0 and internal energy are calculated. We found clear phase transition in the RG flow. The internal energy shows clear deconfinement transition. It rises from zero in low T to a finite value in high T. It shows approximate Stefan-Boltzmann law in high T region. Migdal RG approach including fermion is postponed for future studies.2. Non-perturbative method found in studies of quantum chromo dynamics is applied to quantum gravity. The gravity with higher derivatives is expressed by 0(4) variables. By rewriting them by variables with SU(2)xSU(2) gauge symmetry, it is shown the symmetry is spontaneously broken. The Einstein term arises as a result.3. The Lagrangian including coordinates which are bounded is quantized in the path integral method. According to Faddeev-Senjanovic method, namely by introducing the constraint in <delta> -function form, the quantum Hamiltonian of the system on D-dimensional sphere is obtained.

1.用Migdal重整化群方法研究了有限温度下的格点规范理论。从各种裸耦合常数定义的各种裸理论出发，经过足够多的Migdal RG变换，我们得到了一个唯一的重整化理论。这种行为可以用对应于无限个不可约表示的无限个耦合常数的集合来观察。每一个作用都用无穷维耦合常数空间中的一个点来表示。RG变换将点驱动到独立于裸作用的唯一重整化轨迹。T=0时的Migdal RG变换由各向同性尺度变换表示。为了研究T<>0系统，需要在类时方向上的尺度固定的情况下进行非对称尺度变换。我们研究了T<>0时SU（2）和SU（3）的LGT。计算了T<>0时的RG流和内能。我们发现在RG流中存在明显的相变。内能表现出明显的退禁闭转变。它从低T时的零上升到高T时的有限值。在高T区近似为Stefan-Boltzmann定律。考虑费米子的Migdal RG方法被推迟到未来的研究中。将量子染色体动力学研究中的非微扰方法应用到量子引力中。具有较高导数的重力由0（4）个变量表示。通过用SU（2）xSU（2）规范对称性变量重写它们，证明了规范对称性是自发破缺的。爱因斯坦项作为结果出现。3.用路径积分方法对包含有界坐标的拉格朗日量进行量子化。根据Faddeev-Senjanovic方法，即通过引入函数形式的约束<delta>，得到了D维球上系统的量子哈密顿量。