THE CRITERION FOR FRACTIONAL CHARGE OF(1+1)-DIMENSIONAL DIRAC FIELD

The fractional fermion number (charge) of (1+1)-dimensional Dirac field interacting with a scalar background field is investigated. By means of the correspondence principle in (1+1)-dimensional field theory,it is shown that only when the background field develops a solitvn with a node can the fractional fermion number be induced(node theorem).Consistently, a zero mode bound state of the fermion field should be present and responsible for the fractional charge as long as the soliton satisfies certain conditions (theorem of zero mode).We have also obtained the analytical expression of the vacuum charge distribution in the vicinitu of distorted reqion.     

A SOLVABLE 1+1-DIMENSIONAL U(1) GAUGE THEORY

A 1+1-dimensional U(1+1) gauge theory is proposed and the exact solution of its spectrum and corresponding energy eigenstates is found.     

浅论亥姆霍兹定理在电磁场理论中的贯穿作用

讨论了亥姆霍兹定理的表述形式及其在电磁场理论教学中的贯穿作用．根据亥姆霍兹定理，可以由麦克斯韦方程组自然地引出标量电位和矢量磁位函数，并可方便地导出库仑定律或毕奥一萨伐定律，以及位函数与场在自由空间的积分表达式．     

TWO-PARTICLE BOUND STATES IN THE QUANTUM SINE-GORDON FIELD THEORY IN (D+1) DIMENSIONS

The two-particle states of the quantum sine-Gordon fields are studied variationally in (D+1) dimensions using the Gaussian wave functional approach. In both (1+1) and (2+1) dimensions, there exist two-particle bound states for certain ranges of coupling constant, where the vacuum states are stable. In the higher dimensions (D > 2), this approximation indicates that the two-particle states may be only the states consisting of two free particles, which is conformable to the triviality of the sine-Gordon field theory previously obtained in recent literatures.     

对应性原理和玻尔原子模型

回顾玻尔原子模型建立的背景以及玻尔理论的基本原理,阐述玻尔利用对应性原理,创造性地在宏观与微观之间架起连接的桥梁,从而解释原子结构的稳定性和原子光谱规律.     

A(1+1)-DIMENSIONAL LATTICE U(1) GAUGE MODEL AND THE FERMION SPECIES DOUBLING

A(1+1)-dimensional lattice U91) gauge model with fermion species doubling is solved exactly.The results show that doubling exists for meson states composed of fermions and antifermions.Furthermore we prove that Susskind fermions can beat the doubling of meson states.     

n+1维双sine-Gordon模型的Coleman相变

本文计算了n+1维双sinc-Gordon模型的高斯有效势,在高斯有效势近似下,证明:n≥3的模型是平凡的,n<3的模型存在一个Coleman相交点,临界耦合参数为β_cr=(2ⁿ⁺²π^(n+1)/2(α_1R+α_2R/4)^(3-n)/2)/(Γ(1/2(3-n))(α_1R+α_2R/16)). 关键词：     

隐变量理论与Bell定理

本文详细地讨论了隐变量自旋关联、量子力学自旋关联、Ｂｅｌｌ定理及其意义．     

复合场场论和层子模型(Ⅰ)

本文将文献中所探讨的复合场场论推广到基本场量是旋量场的情形,并由此给出了层子模型理论中有关介子体系所用到的各种公式。     

Reissner-Nordstrom几何中标量场的统计熵与能斯特定理

从Reissner-Nordstrom时空背景下的Klein-Gordon方程出发,利用改进的brick-wall方法膜模型,计算黑洞背景下标量场的自由能和熵.得到标量场的熵是由两部分组成的,根据熵是广延量的性质,得到黑洞熵是由两个子热力学系统贡献的.在此基础上给出了新的Bekenstein-Smarr公式.结果表明,用两个子热力学系统表达的熵,当黑洞的辐射温度趋于绝对零度时,黑洞的熵也趋于零,它满足能斯特定理,可视为黑洞的普朗克绝对熵. 关键词： brick-wall方法 膜模型 黑洞熵 能斯特定理     

SIMILARITY REDUCTIONS OF THE (2+1)-DIMENSIONAL BURGERS SYSTEM

In this paper, using the direct method of the (2+1)-dimensional multi-component Burgers system, some types of similarity reductions are obtained. The corresponding group explanations of the reductions, Virasoro integrability and soliton solutions of Burgers system are also discussed.     

扇形重叠场中三级离子轨迹理论(Ⅱ)——变换矩阵、刘维定理和转换矩阵

本文讨论了扇形重叠场的三级离子光学理论,给出了重叠场的三级变换矩阵,证明它们的行列式为1,从而刘维定理在三级近似计算中成立,引入了转换矩阵以实现变换矩阵在不同分散形式间的转化,对于径向三级离子轨迹及其斜率的展开式中的系数矩阵(S和H矩阵),推导了它们一些元素间的等式及对应关系,这些结果对于离子光学的理论研究和质谱仪器的实际设计有一定的意义。 关键词：     

（2+1）维NLBQ方程和KP方程的多dromion结构和相互作用的研究

从（2+1）维双线性形式的非局域Bussinesq(NLBQ)方程和KP方程的隐线孤子解出发,可以找到与某种势所相应的各方向都指数衰减的dromion解.利用图形分析的方法,对这些dromion之间的相互作用进行了详细的研究.发现这两种模型中的dromion间的相互作用只引起位相漂移,不引起形状和速度的变化,也不引起旋转.即dromion间的相互作用是弹性的,没有能量、动量和角动量的交换. 关键词：     

一个4+1维宇宙模型

我们讨论的4+1维宇宙模型是通常的四维时空和一个紧致的一维内禀空间的直积空间。我们假定四维时空的能量密度是以辐射为主的,而内禀子空间的能动张量是一个阶跃函数。通过求解五维的Einstein场方程得到前四维时空由de-Sitter解过渡到标准模型的辐射为主解,与此同时内禀子空间的尺度由减幅振荡过渡到为按t的负幂次收缩而趋于一常量。 关键词：     

ON THE CONJUGATE FIELD QUANTITY AND THE DEFINITION OF THE RELATIVISTIC WAVE FUNCTION IN THE COMPOSITE FIELD THEORY

The definition of the conjugate field quantities in the composite field theoryand the possible forms of the relativistic wave functions of the bound state are discus-sed.Possible ways to solve these two problems simultaneously are suggested.     

一维强场模型研究中的非齐线性正则方程的辛算法

就一维强场模型,采用对称差商代替空间变量的2阶偏导数,将含有SchrÖdinger方程的初边值问题离散成"非齐线性正则方程",它的齐方程的通解和非齐方程特解都由"辛变换生成",分别采用辛格式计算.采用这种辛算法和R-K法计算了一个数值例子,并与精确解作了比较.结果表明,经长时间计算后,辛算法保持解的固有特征,而R-K法则面目全非.     

非平衡统计场论与临界动力学(Ⅱ)——拉氏场论表述

本文从闭路格林函数生成泛函的连续积分表示出发,对傅氏变换取单圈近似,求得序参量的有效作用量。在闭路连续积分中取涨落二级近似,得到临界动力学的拉氏场论表述。文中指出改进现有理论的可能途径。 关键词：     

(2+1)-DIMENSIONAL DERIVATIVE NONLINEAR SCHRODINGER EQUATION

A(2+1)-dimensional multi-component derivative nonlinear Schr?dinger (DNLS) equation is obtained from the symmetry constraint of the modified Kadomtsev-Petviashvili equation, The model is proved to be inte- grable under the meaning that it possesses the Paitdevé property and the infinitely many generalized symmetries which constitute a generalized W_∞ algebra, An integrable DNLS hierarchy is obtained from the flow equation of infinitely many symntetries of the DNLS equation.     

电磁波荡器及导引磁场中相对论电子三维运动的线性与非线性分析

本文详细地分析处于圆波导TE_mn模(或TM_mn模)及导引磁场中相对论性电子的三维运动。给出线性解析表达式及非线性数值计算结果。文中发现,通常情况下电子轨道在横平面的投影是圆环,环的厚度取决于电磁波荡器的场幅值;而当电磁波荡器是对称模式(m=0)时,电子轨道有可能发散。文中还讨论电磁波荡器是与电子运动同向传播的慢波这种特殊情况。     

THE MASS GAP IN 2+1 DIMENSIONAL SU(3) LATTICE CAUGE THEORY

We present a variational calculation of C=+1 and C=－1 glueball masses in 2+1 dimensional SU(3) lattice gauge theory using a Hamiltonian in which the ground state is exactly known.In the range 0<1/g²≤6,we obtain good scaling behaviour am₊=36.1g² and am_－=5.98g².