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 ...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.展开更多
In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin...In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.展开更多
Two factorization approaches have been proposed for single transverse spin asymmetries. One is the cofiinear factorization, the other is the transverse-momentum-dependent factorization. They have been previously deriv...Two factorization approaches have been proposed for single transverse spin asymmetries. One is the cofiinear factorization, the other is the transverse-momentum-dependent factorization. They have been previously derived in a formal way by using diagram expansion at hadron level. If the two factorizations hold or can be proven, they should also hold when we replace hadrons with patton states. We examine these two factorizations at patton level with massless partons. It is nontrivial to generate these asymmetries at parton level with massless patrons because the asymmetries require helicity-flip and nonzero absorptive parts in scattering amplitudes. By constructing suitable patton states with massless partons we derive the two factorizations for the asymmetry in Drell-Yan processes. It is found from our results that the collinear factorization derived at parton level is not the same as that derived at hadron level. Our results with massless partons confirm those derived with single massive parton state in our previous works.展开更多
In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields...In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.展开更多
文摘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.
基金The project supported by the State Key Project of Fundamental Research of China under Grant No. G2000067101
文摘In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10721063, 10575126, and 10975169
文摘Two factorization approaches have been proposed for single transverse spin asymmetries. One is the cofiinear factorization, the other is the transverse-momentum-dependent factorization. They have been previously derived in a formal way by using diagram expansion at hadron level. If the two factorizations hold or can be proven, they should also hold when we replace hadrons with patton states. We examine these two factorizations at patton level with massless partons. It is nontrivial to generate these asymmetries at parton level with massless patrons because the asymmetries require helicity-flip and nonzero absorptive parts in scattering amplitudes. By constructing suitable patton states with massless partons we derive the two factorizations for the asymmetry in Drell-Yan processes. It is found from our results that the collinear factorization derived at parton level is not the same as that derived at hadron level. Our results with massless partons confirm those derived with single massive parton state in our previous works.
文摘In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.
