51 research outputs found

    The generation of the (k-1)-dimensional defect objects and their topological quantization

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    In the light of ϕ\phi --mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are investigated. It is pointed out that the topological quantum numbers of the defects are described by the Winding numbers of ϕ\phi --mapping which are determined in terms of the Hopf indices and the Brouwer degrees of ϕ\phi--mapping. Furthermore, it is shown that all the topological defects are generated from where ϕ=0\vec \phi =0, i.e. from the zero points of the ϕ\phi --mapping.Comment: 10 pages, LaTe

    SO(4) Monopole As A New Topological Invariant And Its Topological Structure

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    By making use of the decomposition theory of gauge potential, the inner structure of SU(2) and SO(4) gauge theory is discussed in detail. We find the SO(4) monopole can be given via projecting the SO(4) gauge field onto an antisymmetric tensor. This projection fix the coset SU(2)/U(1)% SU(2)/U(1)\bigotimes SU(2)/U(1) of SO(4) gauge group. The generalized Hopf map is given via a Dirac spinor. Further we prove that this monopole can be consider as a new topological invariant. Which is composed of two monopole structures. Local topological structure of the SO(4) monopole is discussed in detail, which is quantized by winding number. The Hopf indices and Brouwer degree labels the local property of the monopoles.Comment: 17 pages, Revtex, no figure

    The Bifurcation of the Topological Structure in the Sunspot's Electric Topological Current with Locally Gauge-invariant Maxwell-Chern-Simons Term

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    The topological structure of the electric topological current of the locally gauge invariant Maxwell-Chern-Simons Model and its bifurcation is studied. The electric topological charge is quantized in term of winding number. The Hopf indices and Brouwer degree labeled the local topological structure of the electric topological current. Using Φ\Phi -mapping method and implicity theory, the electric topological current is found generating or annihilating at the limit points and splitting or merging at the bifurcate points. The total electric charge holds invariant during the evolution.Comment: 13 page, revte

    Strings and the Gauge Theory of Spacetime Defects

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    we present a new topological invariant to describe the space-time defect which is closely related to torsion tensor in Riemann-Cartan manifold. By virtue of the topological current theory and ϕ\phi-mapping method, we show that there must exist many strings objects generated from the zero points of ϕ\phi-mapping, and these strings are topological quantized and the topological quantum numbers is the Winding numbers described by the Hopf indices and the Brouwer degrees of the ϕ\phi-mapping.Comment: 12 pages, no figures, LaTeX. Int. J. Theor. Phys., to appear in 1999, No.

    The General Decomposition Theory of SU(2) Gauge Potential, Topological Structure and Bifurcation of SU(2) Chern Density

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    By means of the geometric algebra the general decomposition of SU(2) gauge potential on the sphere bundle of a compact and oriented 4-dimensional manifold is given. Using this decomposition theory the SU(2) Chern density has been studied in detail. It shows that the SU(2) Chern density can be expressed in terms of the δ\delta -function δ(ϕ)\delta (\phi) . And one can find that the zero points of the vector fields ϕ\phi are essential to the topological properties of a manifold. It is shown that there exists the crucial case of branch process at the zero points. Based on the implicit function theorem and the taylor expansion, the bifurcation of the Chern density is detailed in the neighborhoods of the bifurcation points of ϕ\phi. It is pointed out that, since the Chren density is a topological invariant, the sum topological chargers of the branches will remain constant during the bifurcation process.Comment: revtex, 21pages, no figur

    The topological quantization and the branch process of the (k-1)-dimensional topological defects

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    In the light of ϕ\phi-mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are obtained under the condition that the Jacobian J(ϕ/v)0J(\phi/v) \neq 0. When J(ϕ/v)=0J(\phi/v)=0, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, we detail the bifurcation of generalized topological current and find different directions of the bifurcation. The arbitrary dimensional topological defects are found splitting or merging at the degenerate point of field function ϕ\vec \phi but the total charge of the topological defects is still unchanged.Comment: 17 pages, no figure, LATEX fil

    Novel Theory for Topological Structure of Vortices in BEC

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    By making use of the ϕ\phi -mapping topological current theory, a novel expression of ×V\nabla \times \vec{V} in BEC is obtained, which reveals the inner topological structure of vortex lines characterized by Hopf indices and Brouwer degrees. This expression is just that formula Landau and Feynman expected to find out long time ago. In the case of superconductivity, the decomposition theory of U(1) gauge potential in terms of the condensate wave function gives a rigorous proof of London assumption, and shows that each vortex line should carry a quantized flux. The ϕ\phi -mapping topological current theory of ×V\nabla \times \vec{V} can also gives a precise bifurcation theory of vortex lines in BEC

    The second Chern class in Spinning System

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    Topological property in a spinning system should be directly associated with its wavefunction. A complete decomposition formula of SU(2) gauge potential in terms of spinning wavefunction is established rigorously. Based on the ϕ\phi -mapping theory and this formula, one proves that the second Chern class is inherent in the spinning system. It is showed that this topological invariant is only determined by the Hopf index and Brouwer degree of the spinning wavefunction.Comment: 9 pages, no figures, Revte

    The topological quantization and bifurcation of the topological linear defects

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    In the light of ϕ\phi-mapping method and topological current theory, the topological structure and the topological quantization of topological linear defects are obtained under the condition that the Jacobian J(ϕ/v)0J(\phi/v) \neq 0. When J(ϕ/v)=0J(\phi/v) = 0, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of ϕ\phi-mapping, respectively.Comment: 10 pages, no figures, LATEX fil

    Topological quantum mechanics and the first Chern class

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    Topological properties of quantum system is directly associated with the wave function. Based on the decomposition theory of gauge potential, a new comprehension of topological quantum mechanics is discussed. One shows that a topological invariant, the first Chern class, is inherent in the Schr\"odinger system, which is only associated with the Hopf index and Brouwer degree of the wave function. This relationship between the first Chern class and the wave function is the topological source of many topological effects in quantum system.Comment: 12 pages, Revte
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