电单极子和磁单极子的统一模型

证明磁单极子和电单极子可以在Hopf丛(S³=S²×S¹)的基础上统一生成,该丛有结构群U(1).它在底流形S²上的联络可以分为电单极型和磁单极型两类.磁荷有量子化条件而电单极子就是磁量子数n=0时的解.这样,电单极子和磁单极子在理论上具有同一性.它们是同一事物的两种不同的形态.通过映射的伦移引入时间坐标,从而使电单极子成为Minkowski空间中的一个〈活化〉的模型.它具有Lorentz变换下的不变性.     

相对论核多体理论中的自洽问题和求和规则

着重讨论了建立在相对论平均场基态上的相对论无规位相近似的自洽处理 .自洽处理要求基态和巨共振激发态的研究从同一个拉氏量出发,采用同一种建立在相对论下的完备基上的近似 .同时也讨论了自洽条件下Dirac海核子态的作用 ,指出 Dirac海核子态的贡献不能忽略 ,特别是在核的巨单极共振的情况.用约束的相对论平均场方法得到核的巨单极共振的能量逆权重的求和规则 ,从数值上验证了 Dirac海核子态的贡献. A consistent treatment is extremely important in relativistic approaches. We emphasized the consistent approach in relativistic random phase approximation built on relativistic mean filed ground states. The consistent treatment requires that the studies of the ground state and excited states of giant resonances are based on same effective Lagrangian, and on a same complete set of basis. It was found that the effect of the Dirac states could not be neglected, especially in the case of giant...     

Complex Maxwell's equations

A unified complex model of Maxwell’s equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell’s equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac’s quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell’s equations to include longitudinal waves.A formal analogy between this formulation and Dirac’s equation is also discussed.     

Large-Scale Shell Model for Nuclear Structure and Nuclear Astrophysics Studies

The study of neutron-rich nuclei near 132Sn is interesting and important for both nuclear  structure and nuclear astrophysics. For a considerably large model space allowing cross-shell excitations, a new effective Hamiltonian is determined by employing the extended pairing-plus-quadrupole model with monopole corrections. Calculations for two mass regions, for the north-east quadrant of 132Sn with Z > 50 and N > 82 and for the south-west quadrant with Z < 50 and N < 82, have been performed recently. The structure of these nuclei is analyzed in detail, and the role of the monopole corrections canbe clearly seen.     

Smarr’s formula for black holes with non-linear electrodynamics

It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarrs formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayón–Beato and García [1], showing that in the case that variations of the electric charge are involved, the Smarrs formula is no longer valid.     

On First-order Corrections to the LSW Theory II: Finite Systems

We consider first–order corrections to the classical theory by Lifshitz, Slyozov and Wagner (LSW) for systems with a finite number of particles. Numerical simulations in V. E Fradkov etal. [Phys. Rev. E 53:3925–3932 (1996)] show a cross–over in the scaling of the correction term from ^1/3 to ^1/2 ( is the volume fraction of particles), when the system size becomes larger than the screening length. We rigorously derive this cross–over for the rate of change of the energy, starting from the monopole approximation. The proof exploits the fact that the rate of change of energy has a variational characterization.     

The Three-Dimensional Dirac Oscillator in the Presence of Aharonov-Bohm and Magnetic Monopole Potentials

No Heading We study the Dirac equation in 3+1 dimensions with non-minimal coupling to an isotropic radial three-vector potential and in the presence of a static electromagnetic potential. The space component of the electromagnetic potential has angular (non-central) dependence such that the Dirac equation separates completely in spherical coordinates. We obtain solutions for the case where the three-vector potential is linear in the radial coordinate (Dirac oscillator) and the time component of the electro-magnetic potential vanishes. The relativistic energy spectrum and spinor eigenfunctions are obtained.     

A virial approach to soliton-like solutions of coupled non-linear differential equations including the ’t-Hooft-Polyakov monopole equations

A virial theorem for solitons derived by Friedberg, Lee and Sirlin is used to reduce a system of second order equations to an equivalent first order set. It is shown that this theorem, when used in conjunction with our earlier observation that soliton-like solutions lie on the separatrix, helps in obtaining soliton-like solutions of theories involving coupled fields. The method is applied to a system of equations studied extensively by Rajaraman. The ’t-Hooft-Polyakov monopole equations are then studied and we obtain the well-known monopole solutions in the Prasad-Sommerfeld limit (λ=0); for the case λ≠0, we succeed in obtaining a non-trivial algebraic constraint between the fields of the theory.     

单极巨共振弛豫过程

用BNV方程讨论了中能重离子反应形成的热核单极巨共振(GMR)的驰豫过程.计算表明,球形热核GMR振荡是各向同性的,共振能与E_GMR=80A^－1/3公式给出的数值基本一致.核子碰撞和粒子逃逸是引起热核GMR阻尼衰减的主要原因.     

A Gauge Theoretical View of the Charge Concept in Einstein Gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension /l ², the mass parameter of a particle dimension /l, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi–electric monopole charge of the time translation whereas the NUT parameter is a quasi–magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.