由正负磁单极对相互作用诱导的孤立狄拉克弦

基于三维旋量Gross-Pitaevskii(GP)方程研究在含时周期性外磁场作用下玻色-爱因斯坦凝聚体的动力学行为.结果显示,在含时周期外磁场的作用下,铁磁态自旋为1的玻色-爱因斯坦凝聚体将发生拓扑形变.当磁场的两个零点进入凝聚体后,自旋向上态的密度布居图在z轴上分别形成向上和向下的凸起.随着磁场的两个零点在凝聚体内...     

Nucleon octet in a relativistic logarithmic potential

A simple independent-quark-model based on the Dirac equation with logarithmic potential is used to calculate several properties of octet baryons such as magnetic moment, the axial vector coupling constantg _A (n) for neutronβ-decay and the charge radius of the proton. In view of the simplicity of the model, the results obtained are quite good.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

We derive the basic canonical brackets amongst the creation and annihilation operators for a two （1 ＋ 1）- dimensional （2D） gauge field theoretic model of an interacting Hodge theory where a U（1） gauge field （Aμ） is coupled with the fermionic Dirac fields （ψ and ψ）. In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries （and the concept of their generators） that are present in the theory. We do not use the definition of the canonical conjugate momenta （corresponding to the basic fields of the theory） anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries （and corresponding generators） provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.     

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation,then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.     

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

Eigenvalues of the Kählerian Dirac Operator

We get estimates on the eigenvalues of the Kählerian Dirac operator in terms of the eigenvalues of the scalar Laplace–Beltrami operator. In odd complex dimension, these estimates are sharp, in the sense that, for the first eigenvalue, they reduce to Kirchberg's inequality.     

Legendre Transformation for Regularizable Lagrangians in Field Theory

Hamilton equations based not only upon the Poincaré–Cartan equivalent of a first-order Lagrangian, but also upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton–De Donder theory, but regularizable in this generalized sense are studied. Legendre transformation for regularizable Lagrangians is proposed and Hamilton equations, equivalent with the Euler–Lagrange equations, are found. It is shown that all Lagrangians affine or quadratic in the first derivatives of the field variables are regularizable. The Dirac field and the electromagnetic field are discussed in detail.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper.Firstly,since the Dirac equation is described as a matrix equation in phase space,it is necessary to define the Wigner function as a matrix function in spinor space.Secondly,the matrix form of the Wigner function is proven to support the Dirac equation.Thirdly,by solving the Dirac equation,energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.