平移群上同调与Kronecker映象

本文利用任意n维平直空间(平移群流形)到n维球Sⁿ的Kronccker映象,给出平移群的任意高阶同调群上闭链的明显表达式。映象的拖回可作物理解释。 关键词：     

反常、Chern-Simons上链

本文提出一种联络空间上同调的概念,建立这种上同调群与Chern-Simons型示性类系列的同态关系,给出它们在反常、Wess-Zumino有效作用与Schwinger项等问题上的应用;从而概括了Faddeev,宋行长,Zumino等人最近关于这些问题的探讨。 关键词：     

活动标架系下O(n)非线性σ模型Laxpair矩阵的Poisson—Lie结构

在活动标架系下给出了O(n)/O(n-1)对称空间上非线性σ模型的Poisson-Lie括号,并用协变分解的方法讨论了活动标架与固定标架系的协交关系,得到的r、s矩阵可以明显地看出其依赖于场量的部分是由于S^n－1流形上的联络引起的.     

活动标架系下O（n）非线性σ模型Laxpair矩阵的Poisson—Lie结构

在活动标架系下给出了Ｏ（ｎ）／Ｏ（ｎ－１）对称空间上非线性σ模型的Ｐｏｉｓｓｏｎ－Ｌｉｅ括号，并用协变分解的方法讨论了活动标架与固定标架系的协交关系，得到的ｒ、ｓ矩阵可以明显地看出其依赖于场量的部分是由于Ｓｎ－１流形上的联络引起的．     

规范场与主纤维丛上的联络

本文较详细地给出物理上的规范场与数学上的主纤维丛上的联络论之间的对应关系,从而以联络论的观点统一地处理杨振宁所说的规范场的“微分方法”与“积分”方法,并指出存在有更广泛的规范场的可能性。此外,讨论了引力场如何作为规范场及比较了一些已知的引力场方程。     

Berry联络与吴–杨单极势

通过研究一半整数自旋值的中性粒子在球对称磁场中的Born-Oppenheimer方程,发现在自旋空间Berry联络呈非阿贝尔形式.在绝热近似下,Berry联络相当于阿贝尔形式的吴-杨单极场.由于拓扑的非平庸性,利用纤维丛中截面的概念研究了位形空间的动力学,发现中心势场中粒子的角动量和能量均取量子化值,但数值发生移动,这是纯几何起源的现象.     

Berry联络与吴－杨单极势

通过研究一半整数自旋值的中性粒子在球对称磁场中的Ｂｏｒｎ－Ｏｐｐｅｎｈｅｉｍｅｒ方程，发现在自旋空间Ｂｅｒｒｙ联络呈非阿贝尔形式．在绝热近似下，Ｂｅｒｒｙ联络相当于阿贝尔形式的吴－杨单极场．由于拓扑的非平庸性，利用纤维丛中截面的概念研究了位形空间的动力学，发现中心势场中粒子的角动量和能量均取量子化值，但数值发生移动，这是纯几何起源的现象．     

Fraunhofer全息图无透镜再现中的物像共轭关系

运用相因子判断法，导出了Ｆｒａｕｎｈｏｆｅｒ全息图无透镜再现时再现像与再现光源之间满足的物像共轭关系，分析了再现光源位置变更对再现像性质的影响。     

非线性联络论、Beltrami联络与二维引力

本文利用非线性联络的理论,在二维空间中提出Beltrami联络的概念,用这一概念讨论二维Polyakov引力的对称性。 关键词：     

高分辨率空问光学系统位置误差的无波前传感综合校正

高分辨率三反射式空间光学系统的三个镜子之间的相对位置误差会影响整个系统的性能,需要进行空间在轨调校.提出一种新的无波前传感综合校正方法,将随机并行梯度下降算法、相位变更法和灵敏度矩阵反演法相结合,既保留了灵敏度矩阵反演法的校正精度,又大大提高了可校正误差的动态范围.该方法无须使用波前传感器,系统简单,实现容易.对一个典...     

Local Anomalies and Local Equivariant Cohomology

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology. This interpretation allows us to solve the problem proposed by Singer in [31], and consists in defining an adequate notion of local cohomology to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. Moreover, using the relation between local cohomology and the cohomology of jet bundles studied in [19] we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.     

Coeffective and de Rham cohomologies of symplectic manifolds

We discuss the relation of the coeffective cohomology of a symplectic manifold with the topology of the manifold. A bound for the coeffective numbers is obtained. The lower bound is got for compact Kähler manifolds, and the upper one for non-compact exact symplectic manifolds. A Nomizu's type theorem for the coeffective cohomology is proved. Finally, the behaviour of the coeffective cohomology under deformations is studied.     

Remarks on the relation between different (open) string field theories

It is shown that the different three-string vertices, related by conformal transformations, are in the same BRST cohomology class. We use this result to discuss the relation between different (open) string field theories.     

Jet Coordinates for Local BRST Cohomology

The construction of appropriate jet space coordinates for calculating local BRST cohomology groups is discussed. The relation to tensor calculus is briefly reviewed too.     

Cohomology of the Virasoro algebra with coefficients in string fields

The first cohomology of the Virasoro algebra with coefficients in string fields are investigated. The relation between them and the Nambu-Goto action for a closed string is established.     

Quantum Cohomology and the Periodic Toda Lattice

We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional K?hler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. We derive a simple and explicit “differential operator formula” for the necessary quantum products, which applies both to the finite-dimensional and to the infinite-dimensional situations. Received: 20 April 1999 / Accepted: 12 April 2000     

On Hermitian-Holomorphic Classes Related to Uniformization,the Dilogarithm,and the Liouville Action

Metrics of constant negative curvature on a compact Riemann surface are critical points of the Liouville action functional, which in recent constructions is rigorously defined as a class in a ech-de Rham complex with respect to a suitable covering of the surface. We show that this class is the square of the metrized holomorphic tangent bundle in hermitian-holomorphic Deligne cohomology. We achieve this by introducing a different version of the hermitian-holomorphic Deligne complex which is nevertheless quasi-isomorphic to the one introduced by Brylinski in his construction of Quillen line bundles. We reprove the relation with the determinant of cohomology construction. Furthermore, if we specialize the covering to the one provided by a Kleinian uniformization (thereby allowing possibly disconnected surfaces) the same class can be reinterpreted as the transgression of the regulator class expressed by the Bloch-Wigner dilogarithm.     

On the Relation Between Open and Closed Topological Strings

We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology of the category of D-branes. We compute the Hochschild cohomology of the category of D-branes in topological Landau-Ginzburg models and partially verify the conjecture in this case.Acknowledgement A.K. would like to thank Volodya Baranovsky, Ezra Getzler, Kentaro Hori, Dima Orlov, and Sasha Voronov for help at various stages. A.K. is also grateful to the Department of Mathematics of Northwestern University and the Erwin Schrödinger Institute for hospitality while this work was being completed. L. R. is very grateful to Mikhail Khovanov for numerous discussions of the category of matrix factorizations. This work was supported in part by the DOE grant DE-FG03-92-ER40701 and by the NSF grant DMS-0196131.     

Two-loop superstrings VII. Cohomology of chiral amplitudes

The relation between superholomorphicity and holomorphicity of chiral superstring N-point amplitudes for NS bosons on a genus 2 Riemann surface is shown to be encoded in a hybrid cohomology theory, incorporating elements of both de Rham and Dolbeault cohomologies. A constructive algorithm is provided which shows that, for arbitrary N and for each fixed even spin structure, the hybrid cohomology classes of the chiral amplitudes of the N-point function on a surface of genus 2 always admit a holomorphic representative. Three key ingredients in the derivation are a classification of all kinematic invariants for the N-point function, a new type of 3-point Green's function, and a recursive construction by monodromies of certain sections of vector bundles over the moduli space of Riemann surfaces, holomorphic in all but exactly one or two insertion points.     

Cohomology of Canonical Projection Tilings

We define the cohomology of a tiling as the cocycle cohomology of its associated groupoid and consider this cohomology for the class of tilings which are obtained from a higher dimensional lattice by the canonical projection method in Schlottmann's formulation. We prove the cohomology to be equivalent to a certain cohomology of the lattice. We discuss one of its qualitative features, namely that it provides a topological obstruction for a generic tiling to be substitutional. We develop and demonstrate techniques for the computation of cohomology for tilings of codimension smaller than or equal to 2, presenting explicit formulae. These in turn give computations for the $K$-theory of certain associated non-commutative C ^* algebras. Received: 24 June 1999 / Accepted: 18 October 2001