Finsler Geometry and Relativistic Field Theory

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of gauge transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.     

Poisson Reduction and Branes in Poisson–Sigma Models

We analyse the problem of boundary conditions for the Poisson–Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a Poisson algebra that generalizes Diracs construction. The phase space of the model on the strip is related to the (generalized) Dirac bracket on the branes through a dual pair structure.Mathematics Subject Classifications (2000). 81T45, 53D17, 81T30, 53D55.     

Strains and rotations in thin deposited films

Thin films deposited on misfitting substrates exhibit distortions produced by the superposition of coherency strains and the elastic fields of interfacial defects. These distortions become homogeneous strains, ?, and rotations, φ, beyond a characteristic distance from the interface, z, and are partitioned between the film and substrate. Residual strain arises when the density of interfacial defects is insufficient to compensate the intrinsic coherency strain, and is partitioned in a manner depending on the relative thicknesses of the two layers, d. However, rotations are not partitioned in this way. Expressions for the magnitude and partitioning of ? and φ are derived for the case of elastically isotropic materials. Calculated values are shown to be in excellent agreement with experimental measurements for a variety of technologically relevant cases.     

Parity and the spin—statistics connection

A simple demonstration of the spin—statistics connection for general causal fields is obtained by using the parity operation to exchange spatial coordinates in the scalar product of a locally commuting field operator, evaluated at position x, with the same field operator evaluated at − x, at equal times.     

On the CP topological sigma model and the Toda lattice hierarchy

We propose, in bihamiltonian formalism, a version of the Toda lattice hierarchy that is satisfied by the two point correlation functions of the CP¹ topological sigma model at genus one approximation, and we also show that this bihamiltonian hierarchy is compatible with the Virasoro constraints of Eguchi–Hori–Xiong up to genus two approximation.     

The gauging of BV algebras

A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending on the nature of the global symmetry, the gauging involves coupling to a pure ghost system with a varying amount of ghostly supersymmetry. Coupling to an N=0$N=0$ ghost system yields an ordinary gauge theory whose observables are appropriately classified by the invariant BV cohomology. Coupling to an N=1$N=1$ ghost system leads to a topological gauge field theory whose observables are classified by the equivariant BV cohomology. Coupling to higher N$N$ ghost systems yields topological gauge field theories with higher topological symmetry. In the latter case, however, problems of a completely new kind emerge, which call for a revision of the standard BV algebraic framework.     

结构相变的规范场理论

 本文首先从场论的观点出发,构造了完整晶体的拉氏函数——晶体声子场的拉氏函数。利用晶体声子场在局域群G=SO(3)下的对称性破缺,引入了缺陷规范场。借助于场论中的真空对称性自发破缺和缺陷规范场理论,很自然地把缺陷引到结构相变的研究中。我们给出了相变温度θ_c,入点的热容量的跃变值ΔC_v,及序参数Φ_i的计算公式。从公式中,明显可看出缺陷对相变温度、热容变化值及序参数的影响。另外,我们确定了缺陷规范场理论中的耦合常数g。最后,我们给出了由压力引起的结构相变（如冲击相变）的一种可能的机理。     

Al12N、Al12B团簇结构和电子性质的密度泛函计算

利用密度泛函理论研究了Al12N和Al12B团簇的原子结构和电子性质,通过各种异构体的比较,发现两种掺杂团簇的最低能量结构都是完好的二十面体(Ih)结构,N(B)原子占据在二十面体的中心.高对称性团簇形成稀疏离散的电子态密度和大的电子能隙.在Al-N之间发生较大的电荷转移.因此我们建议把Al12N团簇看作是碱金属超原子,Al12B团簇看作是卤素超原子,用来构造团簇组装固体.