TOPOLOGICAL OBJECTS IN THE O(3) NONLINEAR SIGMA MODEL

2007 ◽  
Vol 22 (31) ◽  
pp. 2379-2386
Author(s):  
PENG-MING ZHANG ◽  
XI-GUO LEE ◽  
SHAO-FENG WU ◽  
YI-SHI DUAN
Keyword(s):  
Sigma Model ◽  
Topological Defects ◽  
Current Theory ◽  
Gauge Potential ◽  
Nonlinear Sigma Model ◽  
Dimensional Model ◽  
Vortex Lines ◽  
Dimensional Spacetime ◽  
Topological Current ◽  
Topological Charges

We study the topological defects in the nonlinear O(3) sigma model in terms of the decomposition of U(1) gauge potential. Time-dependent baby skyrmions are discussed in the (2+1)-dimensional spacetime with the CP1 field. Furthermore, we show that there are three kinds of topological defects–vortex lines, point defects and knot exist in the (3+1)-dimensional model, and their topological charges, locations and motions are determined by the ϕ-mapping topological current theory.

Skyrmion Excitations in Graphene

2014 ◽  
Vol 887-888 ◽  
pp. 960-965 ◽  
Author(s):  
Bu Da Zhao ◽  
Ming Xiang
Keyword(s):  
Potential Theory ◽  
Limit Point ◽  
Bifurcation Theory ◽  
Current Theory ◽  
Gauge Potential ◽  
Topological Current ◽  
Mapping Theory

By making use of theφ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the skyrmion excitations of (2+1)-dimensional graphene. It is shown that the topological numbers are Hopf indices and Brower degrees. Based on the bifurcation theory of theφ-mapping theory, it is founded that the skyrmions can be generated or annihilated at the limit point (the generation and annihilation of skyrmion-antiskyrmion pairs).

TOPOLOGICAL ASPECTS OF THE PROTON VORTEX CLUSTERS IN THE CORE OF A NEUTRON STAR

2009 ◽  
Vol 18 (12) ◽  
pp. 1839-1849
Author(s):  
JUN LIANG ◽  
YISHI DUAN
Keyword(s):  
Neutron Star ◽  
Topological Structure ◽  
Order Parameter ◽  
Current Theory ◽  
Bifurcation Points ◽  
The Core ◽  
Topological Current ◽  
London Equation ◽  
Zero Points ◽  
Topological Charges

Based on the ϕ mapping topological current theory, the proton vortex clusters in the core of a neutron star are investigated. We derive rigorously the London equation with topological structure for superconducting protons. We also show that the proton vortices can only stem from the zero points of the vector order parameter. The evolution of the proton vortices is discussed, the proton vortices are found generating or annihilating at the limit points and splitting or merging at the bifurcation points of the vector order parameter, and the total topological charges remain invariant during the evolution.

ANOMALOUS TOPOLOGICAL CURRENT IN THE NONLINEAR SIGMA MODEL

1991 ◽  
Vol 06 (08) ◽  
pp. 1267-1286 ◽  
Author(s):  
KERSON HUANG ◽  
YUJI KOIKE ◽  
JANOS POLONYI
Keyword(s):  
Bound States ◽  
Sigma Model ◽  
World Line ◽  
Coarse Graining ◽  
Nonlinear Sigma Model ◽  
Current Conservation ◽  
Coupling Phase ◽  
Lattice Regularization ◽  
Topological Current ◽  
The Continuum

It is proposed that a classically conserved current may not be conserved in quantum theory due to singular configurations in the path integral. This is illustrated in the (2+1)-dimensional O(3) nonlinear sigma model with lattice regularization. The current here is that of the topological charge density of “Skyrmions”. On the lattice the current is always “anomalous”, due to the existence of Dirac monopoles. The reason is that the world line of a Skyrmion can be regarded as a Dirac string (in a particular gauge), which is terminated by a monopole. Monte-Carlo simulations indicate that, in the continuum limit, current conservation obtains in a weak-coupling phase, in which monopole and anti-monopoles form bound states that disappear upon coarse-graining; but the anomaly persists in a strong-coupling phase, in which the above-mentioned bound states dissociate into a plasma. In the plasma phase rotational invariance will be broken in the presence of a “Hopf term” in the action.

SKYRMION EXCITATIONS OF SPIN HALL EFFECT IN ATOMS

2009 ◽  
Vol 23 (16) ◽  
pp. 1975-1982 ◽  
Author(s):  
JI-BIAO WANG ◽  
JI-RONG REN
Keyword(s):  
Hall Effect ◽  
Bifurcation Point ◽  
Bifurcation Theory ◽  
Atomic System ◽  
Current Theory ◽  
Spin Hall Effect ◽  
Gauge Potential ◽  
Optical Fields ◽  
Topological Current ◽  
Mapping Theory

By making use of ϕ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the skyrmion excitations of spin Hall effect induced by optical fields in neutral atomic system. It is shown that the topological structures of these skyrmions are characterized by ϕ-mapping topological numbers: Hopf indices and Brouwer degrees. Based on the bifurcation theory of ϕ-mapping theory, it is found that the skyrmions can be generated or annihilated at the limit point and they encounter, split or merge at the bifurcation point.

TOPOLOGICAL STRUCTURE OF VORTEX LINES OF QUANTUM ELECTRON PLASMAS IN THREE-DIMENSIONAL SPACE

2009 ◽  
Vol 23 (11) ◽  
pp. 2439-2447
Author(s):  
XUGUANG SHI ◽  
YISHI DUAN
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Current Theory ◽  
Brouwer Degree ◽  
Electron Plasmas ◽  
The Core ◽  
Vortex Lines ◽  
Quantum Electron ◽  
Topological Current ◽  
Three Dimensional Space

The topological properties of quantum electron plasmas in three-dimensional space are presented. Starting from ϕ-mapping topological current theory, the vortex lines are just at the core of wave function obtained. It is shown that the vorticity of the vortex can be expressed by the Hopf index and the Brouwer degree. We find that the vortex lines are unstable in some conditions and the evolution of vortex lines at the bifurcation points is given.

scholarly journals A NEW DESCRIPTION OF COSMIC STRINGS IN BRANE WORLD SCENARIO

2008 ◽  
Vol 23 (24) ◽  
pp. 2023-2030
Author(s):  
YI-SHI DUAN ◽  
LI-DA ZHANG ◽  
YU-XIAO LIU
Keyword(s):  
Magnetic Flux ◽  
Cosmic String ◽  
Cosmic Strings ◽  
Current Theory ◽  
Brane World ◽  
Higgs Model ◽  
Gauge Potential ◽  
Topological Description ◽  
Topological Current ◽  
Effective Description

In the light of ϕ-mapping topological current theory, the structure of cosmic strings are obtained from the Abelian Higgs model, which is an effective description to the brane world cosmic string system. In this topological description of the cosmic string, combining the result of decomposition of U(1) gauge potential, we analytically reach the familiar conclusions that in the brane world scenario the magnetic flux of the cosmic string is quantized and the RR charge of it is screened.

scholarly journals NOVEL TOPOLOGICAL INVARIANT IN THE U(1) GAUGE FIELD THEORY

2007 ◽  
Vol 22 (29) ◽  
pp. 2201-2208 ◽  
Author(s):  
YISHI DUAN ◽  
XINHUI ZHANG ◽  
LI ZHAO
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Potential Theory ◽  
Three Dimensional ◽  
Current Theory ◽  
Topological Invariant ◽  
Gauge Potential ◽  
Gauge Field Theory ◽  
Knot Invariant ◽  
Topological Current

Based on the decomposition of U(1) gauge potential theory and the ϕ-mapping topological current theory, the three-dimensional knot invariant and a four-dimensional new topological invariant are discussed in the U(1) gauge field.

DECOMPOSITION OF SU(2) CONNECTION AND KNOT STRUCTURE IN SKYRME–FADDEEV MODEL

2008 ◽  
Vol 23 (09) ◽  
pp. 1447-1456
Author(s):  
JI-RONG REN ◽  
RAN LI ◽  
YI-SHI DUAN
Keyword(s):  
Current Theory ◽  
Topological Invariant ◽  
Gauge Potential ◽  
Gauge Invariant ◽  
Hopf Invariant ◽  
Linking Numbers ◽  
Vector Decomposition ◽  
Topological Current ◽  
Faddeev Model ◽  
Invariant Principle

In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simple proposal. We also obtain the action of Skyrme–Faddeev model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. Then, the knot structure in Skyrme–Faddeev model is discussed in terms of the so-called ϕ-mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of ϕ-mapping, naturally. At last, we briefly discussed the topological invariant–Hopf invariant which describes the topology of these knots. It is shown that Hopf invariant is the total number of all the linking numbers and self-linking numbers of these knots.

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