Wilson loops in the light of spin networks

If G is any finite product of compact orthogonal, unitary and symplectic matrix groups, then Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group G. If G is orthogonal, unitary or symplectic, then Wilson loops associated to the natural representation of G are enough.

This extends a result of Sengupta [Proc. Am. Math. Soc. 1221 (3) (1994) 897] and earlier work by Durhuus [Lett. Math. Phys. 4 (6) (1980) 515]. In particular, our approach includes the cases of even orthogonal and symplectic groups.     

具有幂率度分布的因特网平均最短路径长度估计

针对具有幂律度分布的复杂网络的平均最短路径长度进行了研究.给出了一个计算因特网平 均最短路径长度的公式.提出因特网的整体构造实质是以最小代价换取最大收益，从此出 发通过对因特网这类复杂网络平均最短路径长度影响因素分析，推断出网络最短路径长度分 布P(l)的基本性质，进而构造了一个只含参数α的P(l)的简洁形式，直接打通了拓扑具有幂 律度分布的因特网的度分布P(k)与网络最短路径长度分布P(l)之间的关系.然后说明了导出 的公式的物理意义，即参数α代表网络节点连接方式和网络的总边数对平均最短路径长 度的影响.此公式意味着只要掌握幂律P(k)～k-α中α值，就可以直接计算相应网 络的平均最短路径长度.通过对已知数据的计算，验证了公式的有效性.阐明了参数 α对网络设计的重要性和对网络功能的影响. 关键词： 复杂网络 幂律 度分布 平均最短路径长度     

苯乙烯和马来酸酐共聚物的13C NMR谱解析和分子链结构表征

通过比较高温110 ℃下特定苯乙烯-马来酸酐共聚物H10和常温紫外辐照特定共聚合的苯乙烯-马来酸酐共聚物UV4的¹³C质子去偶谱和DEPT135谱，总结给出共聚
物链中马来酸酐环中酸酐基的取代效应参数（α=13.5、β=2.5、γ=-2）及引用苯基取代参数：α=16、β=6、γ=-2，对共聚物主链碳的化学位移进行了经验计算，对所有碳，尤其是主链碳在三单元组或四单元组水平上进行了链序列结构归属. 在进行峰面积积分的基础上，对共聚物分子链两种组份摩尔比或摩尔含量、交替度、链嵌段长度、马来酸酐环残基中顺反异构体比和共聚物数均分子量等进行了表征. 共聚物UV4比H10的交替度高许多，表明聚合温度对苯乙烯和马来酸酐共聚合交替链结构的形成有重要影响.     

Gauge Theory on a Discrete Noncommutative Space

In this paper, we apply Connes' noncommutative geometry and the Seiberg—Witten map to a discrete noncommutative space consisting of n copies of a given noncommutative space R ^m . The explicit action functional of gauge fields on this discrete noncommutative space is obtained.     

Geometric Formulation of Gauge Theory of Gravity

Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantumgauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to studythe relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curvedspace, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence betweenquantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gaugetheory of gravity is studied.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

新型CCD显微镜光学系统设计

提出了一种新型的长江作距离短镜筒透射式的ＣＣＤ显微镜，并作了详细地分析，给出该系统的光学设计结果和数据。     

SU(2)纯格点规范场热力学非对称点阵Monte-Carlo模拟

在非对称点阵(ξ=2,3)上模拟了SU(2)纯格点规范场系统的热力学行为,结果表明,非对称点阵Monte-Carlo模拟是实现快速趋向连续物理极限的有效途径.     

Homology in Abelian Lattice Models

We study Abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformulate the theory in terms of different dynamical variables; however, we avoid entirely the use of the dual cell complex. Topological modes which are present in the transformation now appear as homology classes, in contrast to the cohomology modes found in the dual cell picture. Irregularities of dual cell complexes do not arise in this approach. We treat the two and three-dimensional cases in detail, and prove a general vanishing theorem for Wilson line correlators.     

A Note on the Faddeev–Popov Determinant and Chern–Simmons Perturbation Theory

A refined expression for the Faddeev–Popov determinant is derived for gauge theories quantised around a reducible classical solution. We apply this result to Chern–Simons perturbation theory on compact spacetime 3-manifolds with quantisation around an arbitrary flat gauge field isolated up to gauge transformations, pointing out that previous results on the finiteness and formal metric-independence of perturbative expansions of the partition function continue to hold.