51 research outputs found

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

In the light of $\phi$--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 $\phi$--mapping which are determined in terms of the Hopf indices and the Brouwer
degrees of $\phi$--mapping. Furthermore, it is shown that all the topological
defects are generated from where $\vec \phi =0$, i.e. from the zero points of
the $\phi$--mapping.Comment: 10 pages, LaTe

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

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 $% SU(2)/U(1)\bigotimes
SU(2)/U(1)$ 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

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 $\Phi$-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

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 $\phi$-mapping method, we show
that there must exist many strings objects generated from the zero points of
$\phi$-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 $\phi$-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

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 $\delta -$function $\delta (\phi)$. And one can find that the
zero points of the vector fields $\phi$ 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 $\phi$. 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

In the light of $\phi$-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
$J(\phi/v) \neq 0$. When $J(\phi/v)=0$, 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 $\vec \phi$ 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

By making use of the $\phi$-mapping topological current theory, a novel
expression of $\nabla \times \vec{V}$ 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 $\phi$-mapping topological
current theory of $\nabla \times \vec{V}$ can also gives a precise bifurcation
theory of vortex lines in BEC

### The second Chern class in Spinning System

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 $\phi$-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

In the light of $\phi$-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 $J(\phi/v) \neq 0$.
When $J(\phi/v) = 0$, 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 $\phi$-mapping, respectively.Comment: 10 pages, no figures, LATEX fil

### Topological quantum mechanics and the first Chern class

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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