R^(1+1)中Maxwell-Chern-Simons-Higgs模型解的L^(∞)估计

用能量守恒估计和特征线估计的方法解决(1+1)维Maxwell-Chern-Simons-Higgs模型解的Sobolev范数增长性估计问题,给出模型有限能量解的一阶导数的L^(∞)估计,并通过改进指数增长得到解的H^(2)范数的多项式增长.

Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing

The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.

规范场、引力场反常与Chern-Simons链

将规范场和引力场作为两个子流形从而构成一个大的流形．利用ＣｈｅｒｎＳｉｍｏｎｓ链自然地得到规范场反常、各种引力反常以及规范场和引力场之间的相互作用对反常所作的贡献．

Topological aspect of Chern-Simons p-branes

By generalizing the topological current of Abelian Chern Simons （CS） vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field φ（x）, and the topological structure of CS p-branes is characterized by the winding number of the φ-mappings. Furthermore, the Nambu-Goto action and the equation of motion for multi CS p-branes are obtained.

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.

Chern-Simons-Higgs薛定谔方程组解的存在性

对于含有中性标量场及规范位势的非线性薛定谔方程组,当非线性项的增长指数p>2时,该文证明了非平凡解的存在性.

Chern-Simons Landau-Lifshitz模型自对偶方程静态解的存在性

研究了Chern-Simons Landau-Lifshitz模型自对偶方程静态解的存在性问题.首先,利用数学分析理论和分离变量法得到了自对偶方程的静态解.其次,证明了当向量场满足A_(0)=ϕ_(3)-τ时自对偶方程的静态解满足Chern-Simons Landau-Lifshitz方程.最后,利用共变导数和向量运算法则证明了Chern-Simons Landau-Lifshitz模型具有能量守恒和规范不变的性质.

Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction

The Weyl double copy builds the relation between gauge theory and gravity theory, in particular the correspondence between gauge solutions and gravity solutions. In this paper, we obtain the slowly rotating charge solutions from the Weyl double copy for the Kerr black hole with small Chern-Simons correction. Based on the Weyl double copy relation, for the Petrov type D solution in Chern-Simons modified gravity, we find the additional correction to the electromagnetic field strength tensor of the rotating charge. For the Petrov type I solution, we find that the additional electromagnetic field strength tensors have external sources, while the total sources vanish at the leading order.

含Chern-Simons项的旋量电动力学的量子正则对称性

构造了含Chern Simons(CS)项的旋量电动力学的规范变换生成元 .按约束Hamilton系统的Faddeev Senjanovic(FS)路径积分量子化方案 ,给出了该系统Green函数的相空间生成泛函 ;导出了正则Ward恒等式 ;分析了系统的量子守恒角动量 。

η-INVARIANT AND CHERN-SIMONS CURRENT

The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.

Quantal conserved charge in non-Abelian Chern-Simons theories

Based on the global canonical symmetry of the path integral in phase space, the quantal conserved angular momentum and BRS charge for non-Abelian Chern-Simons (CS) theories have been derived. The possibility of the occurrence of fractional spin properties for non-Abelian CS theories cannot be always preserved at the quantum level.

Phantom Dilaton Field and Asymptotic Distribution Parameter in (2+1)-Dimensional Maxwell-Chern-Simons Gravity

The (2+1)-dimensional Maxwell-Chern-Simons gravity with phantom dilaton field coupling is studied in this paper.It is shown that black hole solution to exist when electromagnetic coupled to dilaton field in the non-trivial way.Moreover,asymptotic index and distribution parameter of current density are calculated by using black hole solution,some new features of this solution are briefly discussed.

Chern-Simons Invariant and Conformal Embedding of a 3-Manifold

This note studies the Chern-Simons invariant of a closed oriented Riemannian 3-manifold M. The first achievement is to establish the formula CS（e） - CS（e） = degA, where e and e are two （global） frames of M, and A ： M → SO（3） is the ＂difference＂ map. An interesting phenomenon is that the ＂jumps＂ of the Chern-Simons integrals for various frames of many 3-manifolds are at least two, instead of one. The second purpose is to give an explicit representation of CS（e＋） and CS（e_）, where e＋ and e_ are the ＂left＂ and ＂right＂ quaternionic frames on M3 induced from an immersion M^3 → E^4, respectively. Consequently we find many metrics on S^3 （Berger spheres） so that they can not be conformally embedded in E^4.

Anomalous spin of the Chern-Simons-Georgi-Glashow model

With the Coulomb gauge, the Chern-Simons-Georgi-Glashow （CSGG） model is quantized in the Dirac formalism for the constrained system. Combining the Gauss law and Coulomb gauge consistency condition, the difference between the Schwinger angular momentum and canonical angular momentum of the system is found to be an anomalous spin. The reason for this result lies in the fact that the Schwinger energy momentum tensor and the canonical one have different symmetry properties in the presence of the Chern-Simons term.

Quantal symmetries in the non-linear σ model with Maxwell and non-Abelian Chern-Simons terms

The quantal symmetry property of the CP1 nonlinear （y model with Maxwell non-Abelian Chern- Simons terms in （2＋1） dimension is studied. In the Coulomb gauge, the system is quantized by using the Faddeev-Senjanovic （FS） path-integral formalism. Based on the quantaum Noether theorem, the quantal conserved angular momentum is derived and the fractional spin at the quantum level in this system is presented.

The Asymptotic Behavior of Chern-Simons Higgs Model on a Compact Riemann Surface with Boundary

We study the self-dual Chern-Simons Higgs equation on a compact Riemann surface with the Neumann boundary condition. In the previous paper, we show that the Chern-Simons Higgs equation with parameter A 〉 0 has at least two solutions （uλ^-, uλ^2） for A sufficiently large, which satisfy that uλ^1 - -u0 almost everywhere as λ →∞, and that uλ^2 →-∞ almost everywhere as λ→∞, where u0 is a （negative） Green function on M. In this paper, we study the asymptotic behavior of the solutions as λ →∞, and prove that uλ^2 - uλ^2- converges to a solution of the Kazdan-Warner equation if the geodesic curvature of the boundary OM is negative, or the geodesic curvature is nonpositive and the Gauss curvature is negative where the geodesic curvature is zero.

Stringy Phenomenology with Preon Models

We compare, following Pati, global symmetries, our topological supersymmetric preon model with the heterotic E8 × E8 string theory. We include Pati’s supergravity based preon model in this work and compare the preon interactions of his model to ours. Based on preon-string symmetry comparison and preon phenomenological results, we conclude that the fundamental particles are likely preons rather than standard model particles. .

The Fate of Supersymmetry in Quantum Field Theories

We analyze the significance of supersymmetry in two topological models and the standard model (SM). We conclude that the two topological field theory models favor hidden supersymmetry. The SM superpartners, instead, have not been found.

From Chern-Simon, Holography and Scale Relativity to Dark Energy

Chern-Simon theory and the holographic principle as well as scale relativity are used to find out the exact value of cosmic ordinary and dark energy density. The result agrees completely with previously obtained ones as well as with accurate cosmic measurements.