The Fibre Bundle Formulation of σ-Model and SUSY σ-Model

In this paper, we present an analysis of the general symmetry properties of some physical systems, where especially the method of h_μ(x), k_μ(x) decomposition of connection is used. Then we reformulate the σ-model and the SUSY σ-model in the framework of fibre bundle theory. By comparisons, we obtain the SUSY partner of "linearized" equation or Lax pair of σ-model.     

A New(γ_A,σ_B)-Matrix KP Hierarchy and Its Solutions

A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(γA,σB)matrix KP hierarchy are studied.The dressing method is generalized to the(γA,σB)-matrix KP hierarchy and some solutions are presented.     

QCD Correction to σ(e+e-→ZH→Zbb)

We study the QCD corrections to the calculated values of σ(e⁺e^-→ZH→Zbb), and find that for M_H<100 GeV, the process can be measured at the LEP energy to extract information of Higgs and the QCD corrections are negligible, namely the tree-level calculation is sufficiently aciurate for the energy range, while for M_H > 100 GeV, the Higgs-involved subprocess can only be investigated at NLC, and then the QCD correction becomes as large as 45%. For M_H > 2mt, considering the subprocess e⁺e^-→ZH→Ztt, the QCD corrections are also important and must be taken into account for the cross section evaluation.     

σ-ω Mixing for the Collective Excitation Spectra of σ, ω Mesons in Nuclear Matter

We study σ-ω mixing on the σ and ω propagators in two ways. The collective excitation spectra of σ,ω mesons are calculated by using these propagators. We find that the two ways of σ-ω mixing give very similar collective excitation spectra in the time-like region.     

ON THE TWO-DIMENSIONAL MON-LINEAR σ MODEL WITH WESS-ZUMINO TERM

The classical solutions of the two-dimensional non-linear σ model with Wess-Zumino term are shown to be equivalent to that without the Wess-Zumino term under a suitable transformation.     

Pion Propagator in the Chiral σ Model of Nuclear Matter

Pion propagator is studied in the chiral σ model at the zero temperature nuclear matter. Due to the tachyon pole of the π and σ tree approximation propagators, only the nucleon polarization insertion loop (explicitly density dependent part and vacuum fluctuation part) can be fully included into the pion propagator. The vacuum fluctuation as a function of nucleon effective mass or pion external momentum (after Wick rotation) is negative for most of the cases. So the variation of nucleon effective mass is restricted to a very limited region where is free of pion condensation (otherwise the nucleon energy density will be complex). The effect of NN short-range correlation is calculated and it is very small for low momentum.     

Wormholes and Non-Linear σ Models

We show that the Giddings-Strominger-like wormholes exist in the systems comprised of SU_L(n)×SU_R(n) or O(n) non-linear a models coupled to O(4) symmetric gravity. Some details are discussed for the case of SU_L(2)×SU_R(2) and two kinds of wormhole instantons are shown.     

基于4A"势能面研究C(3P)+NO(X2Π)→CO(X1Σ+)+N(4S)反应的立体动力学性质

运用准经典轨线方法(QCT), 基于Abrahamsson等构造的⁴A"势能面(Abrahamsson E Andersson S, Nyman G, Markovic N 2008 Phys. Chem. Chem. Phys. 10 4400), 在碰撞能为0.06 eV时, 对C(³P)+NO(X²Π )→CO(X¹Σ⁺)+N(⁴S)反应立体动力学性质进行了理论研究. 在考虑反应物NO转动和振动激发的条件下, 计算了质心坐标系下k-j'矢量(k与j'分别为反应物速度与产物角动量)相关的P(θ_r)分布和k-k'-j'矢量(k'为产物相对速度)相关的P(φ_r)分布. 此外还计算了该反应的三个极化微分截面(2π/σ)(dσ₀₀/dω_t), (2π/σ)(dσ₂₀/dω_t)以及(2π/σ)(dσ₂₂+dω_t). 计算结果表明转动和振动激发对产物取向影响较大而对定向影响较小; 对于三个极化微分截面, 转动激发的影响不大, 而振动激发的影响则较大.     

A New CKP Hierarchy with Two Generalized Time Series and ItsReduction

A new C-type subhierarchy for KP hierarchy with two new time series γ_n and σ_k ((γ_n,σ_k)-CKPH), which consists of γ_n-flow,σ_k-flow and mixed γ_n and σ_kevolution equations of eigenfunctions, is proposed. The zero-curvature representation for the (γ_n,σ_k)-CKPH is derived. The reduction and constrained flows of (γ_n,σ_k)-CKPH are studied.     

Pion and σ-meson Properties in a Strong Magnetic Field

With the Nambu-Jona-Lasinio (NJL) model we calculate the properties of pion and σ-meson at finite temperature and finite magnetic field. The obtained temperature and magnetic field strength dependence of the constituent quark mass M, the pion and σ-meson masses and the neutral pion decay constant indicates that, in the simple four fermion interaction model, there exists the magnetic catalysis effect. It also shows that the Gell-Mann-Oakes-Renner relation is violated obviously with the increasing of the temperature, and the effect of the magnetic field becomes pronounced only around the critical temperature. The deviation of the critical temperatures obtained with different criteria indicates that the chiral phase transition driven by the temperature in the magnetic field strength region we have considered is in fact a crossover.     

NEB NONLINEAR σ MODELS ON SYMMETRIC SPACES

Two new nonlinear σ models, defined on the symmetric coset spaces GL (n,c). ⊕ GL(n,c)/GL (n,c) and GL (n,c)/U(n) respectively, are formulated in this paper.The latter may be useful in discus-sing the four-dimensional Yang-Mills fields.     

Double Wronskian Solutions for a Generalized Nonautonomous Nonlinear Equation in a Nonlinear Inhomogeneous Fiber

A generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber, is investigated. N-soliton solutions for such an equation are constructed and verified with the Wronskian technique. Collisions among the three solitons are discussed and illustrated, and effects of the coefficients σ₁(x, t), σ₂(x, t), σ₃(x, t) and v(x, t) on the collisions are graphically analyzed, where σ₁(x, t), σ₂(x, t), σ₃(x, t) and v(x, t) are the first-, second-, third-order dispersion parameters and an inhomogeneous parameter related to the phase modulation and gain(loss), respectively. The head-on collisions among the three solitons are observed, where the collisions are elastc. When σ₁(x, t) is chosen as the function of x, amplitudes of the solitons do not alter, but the speed of one of the solitons changes. σ₂(x, t) is found to affect the amplitudes and speeds of the two of the solitons. It reveals that the collision features of the solitons alter with σ₃(x, t)=-1.8x. Additionally, traveling directions of the three solitons are observed to be parallel when we change the value of v(x, t).     

(3 + 1)-Dimensional Integrable Models Possessing Infinite Dimensional Virasoro-Type Symmetry Algebra

Using a series of concrfte reGzations of the centerless Virasoro-type symmetry algebra [σ(ƒ₂(t), σ(ƒ₁(t))] = σ(ƒ₁ƒ₂ - ƒ₂ƒ₁), various (3+1)-dimensional integrable equations under the condition that they possess Kac-Moody-Virasoro-type infinite dimensional symmetry algebra are obtained.     

THE Hn SIGMA-MODELS AND SELF-DUAL SU(n) YANG-MILLS FIELDS IN FOUR-DIMENSIONAL EUCLIDEAN SFACE

The H_n σ-models. i.e., non-linear σ-models taking-values on the symetric coset space SL(n,c)/SU(n), both in two-dimensional and four-dimensional Euclidean space,.are formulated. The relations with self-duel SU(n) Yang-Mills fields are also discussed.     

NONLINEAR σ-MODEL ON MULTID IMENSI CNAL CURVED SPACE WITH CERTAIN CYLINDRICAL SYMMETRY

A dual transformation is found for a class of nonlinear σ-model defined on a multidimensional curved space with cylindrical symmetry. The system is invariant under a proper combination of the dual transformation and the general coordinate transformation. An infinite number of nonlocal conservation laws as well as the Kac-Moody algebra follow directly from the dual transformation. A Backlund transformation that qenerates new solutions from a given. one can also be constructed.     

The Collective Excitation Spectra of σ, ω and π Mesons in Nuclear Matter

The recent progress on the study of the collective excitation in relativistic nuclear matter is reviewed. The collective excitation modes are derived by meson propagators in nuclear matter. The mesons we studied are σ, ω, γ and π mesons. For pion, we derived not only the relativistic particle-hole, delta-hole excitations but also antiparticle excitations, suchas particle-antiparticle, antidelta-particle, delta-antiparticle excitations. By calculating the dispersion relation and the spin-isospin-dependent response function, the effects of all these excitation are studied.     

ALGELRAIC PROPERTIES OF NONLINEAR σ MODEL OF SU(2) WITH W-Z TERM IN 1+1 DIMENSIONS

Taking three Euler angles as the field variables of nonlinear σ model of SU(2),we calculated the Wess-Zumino term and showed by using canonical quantization that the chiral cuirents of this model satisfy a Kac-Moody alqebra at n equal an even intsger for arbitrary value of λ^o.     

Study of the Binding Energy of Relativistic Nuclear Matter in the Relativistic σ-ω-π Model

A relativistic σ-ω-π model is proposed to calculate the binding energy of relativistic nuclear matter. We put emphasis on the relativistic particle-hole, delta-hole excitation of pion propagator in nuclear matter. The renormalization of the nucleon self-energy in nuclear matter is made for the pseudo-vector πNN and πNΔ couplings by introducing corresponding form factor and by dispersion relation. We find that the density dependence correction to meson-NN coupling constants is very important to saturate the binding energy of nuclear matter. The density dependence correction to πNN and πNΔ coupling constants has the effect of softening the EOS of nuclear matter.     

Faddeev-Jackiw Quantization and Its Application to the Linear σ Model for Disoriented Chiral Condensates

The equivalence between the Faddeev-Jackiw formalism and Dirac-Bergmann algorithm is proved. A two-dimensional constrained system and a charged vector field are quantized in the Faddeev-Jackiw formalism. This symplectic method is technically developed, without recourse to Hamiltonian or Lagrangian, to quantize systems whose equations of motion are known. Examples are given to show this role. For constructing quantum approaches to the disoriented chiral condensates, the linear σ model is quantized in the instant form, light-cone form and covariant form.     

O_2分子B~3Σ_u~-态势能曲线的从头计算

B~3Σ_u~-态是O_2的最强的三重跃迁(B~3Σ_u~-←XΣ_g~-)Schumann-Runge(SR)带的上态,SR吸收带在保护地球、阻止紫外辐射等方面起着关键作用.SR连续带的光解离是平流层O原子及O_3的主要来源,掌握详细准确的O_2分子的电子态势能曲线,有助于对这些光谱现象的深入理解.本文通过MOLPRO软件,采用包含Davison修正的内收缩的多参考组态相互作用(ic MRCI+Q)方法,对O2的B~3Σ_u~-态的势能曲线进行了计算,采用的多参考组态函数来自完全活性空间自洽场计算.首先,采用共价组态构成多参考组态,对和B~3Σ_u~-态对称性相同的四个态进行了态平均计算,发现B3Σ_u~-态不存在双势阱结构,文献(Spectrochimica Acta Part A:Molecular and Biomolecular Spectroscopy 2014 124 216)中双势阱的产生是根的振荡(root flipping)造成的,即B~3Σ_u~-态的势能曲线在核间距约为0.2 nm处跳变到能量相近的23?态的势能曲线上.本文中的态平均计算避免了这种根的振荡.接着,采用完全活性空间组态相互作用的方法计算B~3Σ_u~-态的势能曲线,通过改变活性空间的轨道组成,发现带有2π_u轨道电子布居的里德伯组态对B~3Σ_u~-态的束缚态的特征的出现是必不可少的.最后,通过将2π_u轨道加入到活性空间中,实现将相关的里德伯组态加入到多参考组态,对B~3Σ_u~-态的势能曲线进行了icMRCI+Q计算,得到相较于以往的理论计算与实验值更加相近的势能曲线以及光谱常数.本文探讨里德伯组态贡献的过程为如何确定多参考组态相互作用计算中的参考组态、提高理论计算的准确度提供了可以借鉴的途径.