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The New Applications of φ-Mapping Topological Current Theory in the Physics

Author: MoShuFan
Tutor: RenJiRong
School: Lanzhou University
Course: Theoretical Physics
Keywords: Topological current 3D vector field Topological properties Magnetic monopoles Bifurcation point Topological charge Parameter field Soliton Bifurcation theory Unit vector Degenerate Points Function structure topological Gauge potential Segment -related disabilities Quantization Critical point Einstein points Covariant
CLC: O189.1
Type: Master's thesis
Year: 2010
Downloads: 11
Quote: 0
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Abstract


Use of this thesis, Professor Duan Yishi φ- mapping topological current theory and U (1) gauge potential decomposition theory to study the bifurcation theory of magnetic monopoles in the two components of the charged Bose-Einstein system , Chern-Simons ( CS ) of p - film branching process in Aratyn-Ferreira-Zimerman (AFZ) model kink soliton . First , the two components of the charged Bose-Einstein system , we obtain the form of the dynamics of magnetic monopoles and (? ) Quantum magnetic charge for the the topological energy levels of the units . Topological quantum number is determined by the Hopf index and Brouwer degree . Topology attributes of magnetic monopoles from the three-dimensional vector field (?) And found that there are critical branching process when D ((?)) ≠ 0 Shi , the evolution of the magnetic monopole . This means that the magnetic monopole in the critical point of the three-dimensional vector field (?) Creation and annihilation meet at the bifurcation point , fission and fusion , showing the instability in these branch point magnetic monopole . Meanwhile, from the topological properties of the three - dimensional vector field (?) Obtained when the magnetic monopole creation and annihilation rate is infinite . In addition, we noted that there are two constraints : the evolution of the magnetic monopole is a conservation of the topological charge of the branching process ; Another is the number of different directions at the bifurcation point magnetic monopole world line up four . Secondly , the application φ- mapping topological current theory , we show the CS p- film produced in the order parameter field ( ?) Of zero , when the order parameter field ( ?) Zero is a normal point , the topological charge by φ- mapping Brouwer degree and Hopf index is quantized . Critical point in the order parameter field ( ? ) , For example, the limit point and bifurcation point , branching process defects topology flow bifurcation . CS p- film as a point of division or fusion means CS p- film at these points is unstable . Finally, we are committed to the the kink soliton the AFZ model in the . Application of U (1) gauge potential decomposition theory and φ- mapping topological current theory detailed study of the the soliton topological properties of the the AFZ model of kink , extraordinary Hopf covariant internal topology .

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CLC: > Mathematical sciences and chemical > Mathematics > Geometry, topology > Topology ( the situation in geometry ) > General topology
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