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 spinor is studied. Using thisdecomposition, the spinor structures of Chern-Simons form and the Chern density are obtained. Furthermore, the knotquantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the secondChern number is characterized by the Hopf indices and the Brouwer degrees of φ-mapping.     

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

Topological structure of the solitons solution in SU（3） Dunne-Jackiw-Pi-Trugenberger model

By using C-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU（N） Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU（3） case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of C-mapping. In our solution, the flux of this soliton is naturally quantized.     

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 b-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.     

A gauge theory for two-band model of Chern insulators and induced topological defects

In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_xy=e²/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.     

Observation of F = 2 Spinor Bose-Einstein Condensation in a Magnetic Field

Multiple-component Bose-Einstein condensation has been observed in a magnetic field generated by a controllable magnetic quadrupole-Ioffe-configuration trap. Different distributions of atoms in spinor Bose Einstein condensates are created by changing the time difference of switching-off current in quadrupole-Ioffe-configuration coils and bias coils of the magnetic trap. A simple analysis is carried out to explain some phenomena of the experiment.     

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

SO（d,d;Z) Transformation Property for Gauge Fluxes and Ramond-Ramond Fields in Noncommutative Geometry

In this paper we study the spinor constructions of gauge fluxes and Ramond-Ramond fields on noncommutative tori T^d up to d=6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced.So that we can express the Chern-Simons Lagrangian in toroidal compactification as a product of spinors.     

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using φ-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of φ-mapping. In our solution, the flux of this soliton is naturally quantized.     

SU(2)Chern-Simons涡旋解的拓扑结构

运用规范势分解理论研究了 Dunne Jackiw Pi Trugenberger 模型中的自对偶方程, 得到一个静态的自对偶Chern Simons多涡旋解, 每个涡旋由5个参数描述。 发现了自对偶解与拓扑数之间的关系, 而拓扑数由Brouwer度与Hopf指标确定。 同时, 也研究了该涡旋解的磁通量的拓扑量子化。The self dual equation and its solution in SU(2) Dunne Jackiw Pi Trugenberger model has Been discussed with special ansatz for the Lie algebraic structures of su(2) and gauge potential decomposition. We obtainer a new concrete self dual equation and found the relationship between SU(2) Chern Simons vortices and topological number which is determined by Hopf indices and Brouwer degrees of  mapping. (two positions, one scale, one phase per vortex and one charge of each vortex) m vortices solutions are discribed by using 5m parameters. The quantization of flux is also studied in this case.     

Quantal Canonical Symmetries in Spinor QED with Chern-Simons Term

The generator of gauge transformation for spinor QED with Chern-Simons (CS) term has been constructed. According to the rule of path integral quantization for constrained system in Faddeev-Senjanovic scheme, the phase-space generating of Green function is obtained, and canonical Ward identities for such a system is also derived. The quantal conserved angular momentum for spinor QED with CS term is studied. The property of fractional spin of the system is pointed out.     

含Chern-Simons项的旋量电动力学的量子正则对称性

构造了含Chern-Simons(CS)项的旋量电动力学的规范变换生成元.按约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,给出了该系统Green函数的相空间生成泛函;导出了正则Ward恒等式;分析了系统的量子守恒角动量,指出它具有分数自旋性质.     

Quantization of the Chern invariant polynomial and its topological quantum ground state

The symplectic quantization of the Chern invariant polynomial on a 2n-dimensional manifold is considered. The ground state wave functional as a representation of the vacuum state of the theory is constructed in terms of the Chern-Simons form. An important consequence of these results is that the existence of the Chern-Simons wave functional is not exclusive of topological four-dimensional gauge theory.     

Three-dimensional fermionic determinants,Chern-Simons and nonlinear field redefinitions

The three-dimensional abelian fermionic determinant of a two component massive spinor in flat euclidean space-time is reset to a pure Chern-Simons action through a nonlinear redefinition of the gauge field.     

A Spinorization of a Constrained Vector System and a Spinor Reconstruction Theorem

An elementary method of conctructing a spinor from vectors satisfying constraint conditions is proposed. We consider orthonormal triad and tetrad as an orientable physical object and introduce parameter representations of them, in terms of the Euler angles and the pseudo-Euler angles. Having determined the transformation property of the parameters, we set up the spinor determining equation. This equation is solved. The solution (spinor) contains four arbitrary complex constants, in 3 + 1 dimensional space. Using the proposed method, we prove the spinor reconstruction theorem, i.e. the original Dirac spinor can be reconstructed from seven of the sixteen hermitian bilinear forms, except the overall phase factor (the gauge freedom of the 1st kind). The energy density of the spinor field is written in terms of currents and their space derivatives.     

THE U(3) ANOMALY

The U(3) anomaly will be given based upon the geometrical and topological method which was used in deterurinating the anomalies for SU(N) and SO(N) gauge fields. It is shown that both the non-Abelian and the Abelian anomaly can be derived in unified treatment from the third Chern class and corresponding Chern-Simons secondary class of the U(3) group.     

Topological Structure of Vortex Solution in Jackiw-Pi Model

By using φ-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.