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。在有限温度下的晶格量规理论（LGT）在Migdal重新归一化组（RG）方法中进行了研究。从各种裸露的耦合常数定义的各种裸露理论开始，我们在足够数量的Migdal RG转换之后，得出了独特的重新归一化理论。通过一组无限数量的耦合常数可以看到这种行为，这些耦合常数对应于无限数量的不可约表示。每个动作都由无限尺寸耦合恒定空间中的一个点表示。 RG转换将点驱动到独特的重新归一化轨迹，而与裸露的动作无关。 T = 0时的Migdal RG转换由各向同性尺度变换表示。为了研究t <> 0系统，必须固定固定方向的比例尺不对称尺度变换。我们调查了t <> 0的SU（2）和SU（3）LGT。 T <> 0的RG流量和内部能量计算。我们发现RG流中的清晰相变。内部能量显示清晰的解料过渡。在高t中，它从低t的零上升到有限的值。它显示了高t区域中的Stefan-Boltzmann定律。包括费米恩在内的Migdal RG方法被推迟以供将来的研究。2。在量子铬动力学研究中发现的非扰动方法应用于量子重力。具有较高衍生物的重力由0（4）变量表达。通过使用SU（2）XSU（2）量规对称性的变量重写它们，显示对称性自发断裂。爱因斯坦的术语结果出现3。在路径积分方法中量化了包含有界坐标的拉格朗日。根据Faddeev-senjanovic方法，即通过在<delta>功能形式中引入约束，可以获得系统的量子哈密顿量在D维球上。