Duan Yi-Shi

Fermion localization and resonances on a de Sitter thick brane

In C. A. S. Almeida, R. Casana, M. M. Ferreira, Jr., and A. R. Gomes, Phys. Rev. D 79, 125022 (2009), the simplest Yukawa coupling eta(Psi) over bar phi chi Psi was considered for a two-scalar-generated Bloch brane model. Fermionic resonances for both chiralities were obtained, and their appearance is related to branes with internal structure. Inspired on this result, we investigate the localization and resonance spectrum of fermions on a one-scalar-generated de Sitter thick brane with a class of scalar-fermion couplings eta(Psi) over bar phi(k)Psi with positive odd integer k. A set of massive fermionic resonances for both chiralities is obtained when provided large coupling constant eta. We find that the masses and lifetimes of left and right chiral resonances are almost the same, which demonstrates that it is possible to compose massive Dirac fermions from the left and right chiral resonances. The resonance with lower mass has longer lifetime. For a same set of parameters, the number of resonances increases with k and the lifetime of the lower level resonance for larger k is much longer than the one for smaller k.

Fermionic Zero Modes in Self-dual Vortex Background on a Torus

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in (5+1) dimensions. Using the generalized Abelian–Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.

Spinor Decomposition of SU(2) Gauge Potential and Spinor Structures of Chern-Simons and Chern Density

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinors is studied. Using this decomposition, the spinor strutures of the Chern-Simons form and the Chern density are obtained. Furthermore, by these spinor structures, the knot quantum number of non-Abelian gauge theory is discussed, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of φ-mapping. PACS number(s): 11.15.−q, 02.40.−k Typeset using REVTEX Author to whom correspondence should be addressed. Electronic address: liuxin@lzu.edu.cn 1In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern-Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of phi-mapping.

The Decomposition of the Gauge Potential and its Quantization Theory

In this presentation, the quantization and renormalization of the Yang-Mills field theory are discussed from the standpoint of the decomposition of gauge potential. It may be regarded as a new basis for the formulation of the fundamental interactions of particle theories.

Topological Constraints on Scroll and Spiral Waves in Excitable Media

A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.

About the Energy of the University

We use the general covariant conservation law of energy-momentum, which is general covariant and therefore preferable to the non-covariant conservation laws, to analyse the energy of the universe and obtained vanishing energy. A physical interpretation of the vanishing energy and some discussions are also presented.

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.

Distribution of topological defects on axisymmetric surface

We propose a general method of determining the distribution of topological defects on axisymmetric surface, and study the distribution of topological defects on biconcave-discoid surface, which is the geometric configuration of red blood cell. There are three most possible cases of the distribution of the topological defects on the biconcave surface: four defects charged with 1/2, two defects charged with +1, or one defect charged with 2. For the four defect charged with 1/2, they sit at the vertices of a square imbedded in the equator of biconcave surface.

Stability of Disclinations in Nematic Liquid Crystals

In the light of -mapping method and topological current theory, the stability of disclinations around a spherical particle in nematic liquid crystals is studied. We consider two different defect structures around a spherical particle: disclination ring and point defect at the north or south pole of the particle. We calculate the free energy of these different defects in the elastic theory. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclinations. The other is the free energy density of disclinations themselves, which is shown to be concentrated at the defect and to be topologically quantized in the unit of (k−k24)π/2. It is shown that in the presence of saddle-splay elasticity a dipole (radial and hyperbolic hedgehog) configuration that accompanies a particle with strong homeotropic anchoring takes the structure of a small disclination ring, not a point defect.

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 -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.