Self-Dual Chern-Simons Vortices in Higgs Field

By decomposing the Bogomol＇nyi self-dual equation in the Abelian Chern-Simons Higgs model, we find a selldual topological term that was ignored all the time in the Bogomol＇nyi self-duality equation due to the improper decomposition of the complex Higgs field. We also present a new self-dual equation that includes the topological term. It is shown that the self-dual vortex just arises from the symmetric phase of the Higgs field φ =0. Using our p-mapping theory, the inner topological structure of the vortex and double vortex is given.     

双折射光纤中非线性耦合Schrdinger方程的小振幅孤波解

采用小振幅孤波近似法，得到非线性耦合Ｓｃｈｒｄｉｎｇｅｒ方程决定的双折射光纤中的小振幅孤波解，它们可以同时存在于正常色散区或者分别处于正常和反常色散区．     

SPACE-TIME TORSION AND THE QUANTIZATION OF SPIN

It is shown that within the framework of the Einstein-Cartan-Sciama-Kibble theory, space-time torsion could account for the quantization of the spin angular momentum of Dirac particles.     

Kl3介子衰变

本文通过强作用K-π中间态,利用色散关系理论计算了Г(K_μ3⁺)/Г(K_α3⁺),Г(K₂⁰→πμ⁺ν)/Г(K₂⁰→πe⁺ν),{Г(K₂⁰→πe⁺ν)+Г(K₂⁰→πe^-ν)}/Г(K_α3⁺)分支比及K_μ3⁺衰变中的μ谱,当选择定则|ΔI|=1/2及ΔS=+ΔQ被破坏,并且I_z=1/2及I_z=3/2的振幅f^{3/2 1/2}(0)及f^{3/2 3/2}(0)不等时,上述分支比与实验能很好符合。在本文的理论中,形式因子不是常数。     

非线性波方程的精确孤立波解

立了一种求解非线性波方程精确孤立波解的双曲函数方法,并在计算机代数系统上加以实现,推导出了一大批非线性波方程的精确孤立波解.方法的基本原理是利用非线性波方程孤立波解的局部性特点,将方程的孤立波解表示为双曲函数的多项式,从而将非线性波方程的求解问题转化为非线性代数方程组的求解问题.利用吴消元法或Gröbner基方法在计算机代数系统上求解非线性代数方程组, 最终获得非线性波方程的精确孤立波解,其中有很多新的精确孤立波解.     

The Topological Inner Structure of Chern-Simons Tensor Current and the World-Sheet of Strings

Using the decomposition theory of U(1) gauge potential and b-mapping topological current theory, we investigate the topological inner structure of Chern Simons tensor current. It is proven that the U(1) Chern-Simons tensor current in four-dimensional manifold is just the topological current of creating the string world-sheets.     

广义相对论中的能量动量守恒定律

本文阐明了在广义相对论中采用半度规表象的必要性,利用半度规数学工具对广义相对论中的守恆定律问题作了比较详细的讨论。从广义位移交换出发,得到了在任何坐标系皆能成立的广义协变的能量动量守恆定律,克服了Einstein,Ландау,M?ller等人关于该方面理论的缺点。 关键词：     

Topological Quantization of Instantons in SU（2） Yang-Mills Theory

By decomposing SU（2） gauge potential in four-dimensional Euclidean SU（2） Yang-Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree. It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.     

Topological structure of Gauss-Bonnet-Chern theorem and -branes

By making use of the φ-mapping topological current theory, this paper shows that the Gauss-Bonnet-Chern density (the Euler-Poincaré characteristic χ(M) density) can be expressed in terms of a smooth vector field φ and take the form of δ(φ), which means that only the zeros of φ contribute to χ(M). This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of -branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi -branes.