Effective Lagrangian of SU（2） Yang—Mills Theory in the Presence of Fermions

We derive the one-loop effective action of SU(2) Yang-Mills theory in the presence of fermions in the low energy limit.This result is presented by separating the topological degrees,which describe the non-Abelian monopoles from the dynamical degrees of the gauge potential and integrate out all the dynamical degrees and fermions in SU(2) Yang-Mills theory.     

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 this decomposition, the spinor structures of Chern Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

Topological Quantization of Instantons in SU（2） Yang-Mills Theory

By decomposing SU（2） gauge potential in four-dimensional Euclidean SU（2） Yang-Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree. It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.     

Thied—Order Approximation of 0^＋＋ Glueball Mass and Wavefunction of （2＋1）—Dimensional SU（3） Lattice Gauge Theory

The random phase approximation is applied to the coupled-cluster expansions of lattice gauge theory (LGT) Using this method,wavefuctions are approximated by linear combination of graplh consisting of only one connected wilson loop.We study the excited state energy and wavelunction in (2 1)-D SU(3) LGT up to the thired order,The glueball mass shows a good scaling behavior.     

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.     

Neutrino Mass Generation in SO（4） Model

Generation of neutrino mass in SO（4） model is proposed here. The algebraic structure of SO （4） is same as to that ofSU（2）L x SU（2）R. It is shown that the spontaneous symmetry breaking results three massive as well as three massless gauge bosons. The standard model theory according to which there exist three massive gauge bosons and a massless one is emerged from this model. In the framework ofSU（2）L x SU（2）R a small Dirac neutrino mass is derived. It is also shown that such mass term may vanish with a special choice. The Majorana mass term is not considered here and thus in this model the neutrino mass does not follow seesaw structure.     

Multi-types of Skyrmions in SU（N） Quantum Hall System

The skyrmions in SU（N） quantum Hall （QH） system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU（N） QH system there can exist （N-1） types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the （N - 1） Cartan subalgebra local bases, we obtain the （N - 1） U（1） electromagnetic field tensors in the SU（N） gauge field of the QH system, and then derive （N - 1） types of skyrmion structures from these U（1） sub-field tensors. Furthermore, in light of the C-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.     

Topological Defects in Liquid Crystal Films

A topological theory of liquid crystal films in the presence of defects is developed based on the Ф-mapping topological current theory. By generalizing the free-energy density in ＂one-constant＂ approximation, a covariant free- energy density is obtained, from which the U（1） gauge field and the unified topological current for monopoles and strings in liquid crystals are derived. The inner topological structure of these topological defects is characterized by the winding numbers of Ф-mapping.     

Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.     

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.     

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.     

Calculation of Vacuum Wavefunction and Mass .Gap from Improved (2+l)-Dimensional SU(2) Lattice Gauge Field Hamiltonian

The truncated eigenvalue equation of SU(N) lattice gauge theory is studied by using improved lattice gauge Hamiltonian with a proper truncation scheme that preserves the continuum limit. The calculations of vacuum state wavefunction and glueball mass of (2+1)-dimensional SU(2) theory up to third order are carried out, the results show the improvement of scaling behavior in deep weak coupling region.     

SU(2)规范场分解与Bose-Einstein凝聚体中的环流条件

利用SU(2)规范场的单位矢量场分解形式讨论了Bose-Einstein凝聚体中的环流条件.对于二分量Bose-Einstein凝聚,内部态的SU(2)对称性将导致一个拓扑环流条件,这是一个推广的Mer-min—Ho关系.     

Coulomb gauge vacua of SU(3) gauge theory

SU(3) gauge field theory is studied in the Coulomb gauge, and the topologically distinct, but gauge equivalent, vacuum configurations are analysed. Considering the gauge transformations of the form U ε U(2) ?SU(3)/U(2), we have obtained a new class of vacuum fields characterized by the topological quantum number η = ±1.     

The Mass Gap of SU(2) Lattice Gauge Theory in 2+1 Dimensions

Coupled cluster expansions are applied to study the eigenvalue problem of the Hamiltonian lattice gauge theory with the orthogonal D-loop basis being used to expand wavefunctions. The 0⁺⁺ bound state wavefunction and its mass gap relative to the vacuum of SU(2) lattice gauge theory in 2+1 dimensions are calculated up to the 7th order.