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

1.用Migdal重整化群(RG)方法研究了有限温度下的格点规范理论。从由各种裸耦合常数定义的各种裸理论出发，经过充分的Migdal RG变换，我们得到了一个唯一的重整化理论。这一行为可以通过一组无限多的耦合常数来看到，这些耦合常数对应于无限多的不可约表示。每个作用都由无限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动作的唯一重新正规化轨迹。T=0时的Migdal RG变换用各向同性标度变换表示。为了研究T&lt；&Gt；0系统，需要在类时间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&lt；&gt；0的SU(2)和SU(3)LGT‘s。计算了T&lt；&gt；0时的RG流量和内能。我们在RG流中发现了明显的相变。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时的一个有限值，在高T区符合近似的Stefan-Boltzmann定律。包括费米子在内的Migdal RG方法将被推迟到未来的研究中。将量子色动力学研究中的非微扰方法应用于量子引力。高阶导数的重力用0(4)个变量表示。通过将它们改写为具有SU(2)xSU(2)规范对称性的变量，表明对称性自发破缺。爱因斯坦这个词就是这样产生的。在路径积分方法中，包含有界坐标的拉格朗日被量子化。根据Faddeev-Senjanovic方法，即通过引入函数形式的约束，得到了D维球上系统的量子哈密顿量。

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.