微分方程的部分Hamilton化与积分

将微分方程部分地表示为Hamilton系统的方程并写成逆变代数形式.用动力学代数建立方程的Poisson积分理论，并举例说明结果的应用. 关键词： 微分方程 部分Hamilton化 逆变代数形式 Poisson积分理论     

构造准正则变换的方法

给出构造Hamilton系统的准正则变换的方法,首先将Hamilton系统变换成Birkhoff系统,然后将Birkhoff系统作规范变换并实现Hamilton化. 指出对一个Hamilton系统存在多种准正则变换. 举例说明所得结果的应用. 关键词： Hamilton系统 准正则变换 Birkhoff系统 规范变换     

含Chern-Simons项的旋量电动力学的量子正则对称性

构造了含Chern-Simons(CS)项的旋量电动力学的规范变换生成元.按约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,给出了该系统Green函数的相空间生成泛函;导出了正则Ward恒等式;分析了系统的量子守恒角动量,指出它具有分数自旋性质.     

单离子各向异性影响下的一维铁磁链中的孤子

利用行波解法，研究了考虑交换各向异性和单离子各向异性的一维铁磁链，得出椭圆函数波解和孤子解,并讨论了单离子各向异性对椭圆函数波和孤子的影响.研究表明：单离子各向异性对一维铁磁链中椭圆函数波和孤子的激发及其稳定性有显著影响.单离子各向异性不利于易轴铁磁链中椭圆函数波和孤子解的激发，但有利于它们的稳定；而在易平面铁磁链中，单离子各向异性使椭圆函数波和孤子激发变得容易，但不利于它们的稳定.此外，还讨论了单离子各向异性对一维各向同性铁磁链中的孤子激发具有的影响. 关键词： 各向异性 单离子各向异性 孤子 铁磁链     

Osp(1,2)自旋链的潜藏定域规范不变性

在量子反散射框架内研究了Osp（1，2）自旋链的潜藏定域规范不变性．结果表明，该模型允许AbelU（1）规范变换，其能谱在规范变换下保持不变，而本征矢及Bethe ansatz方程明显与规范变换相关． 关键词：     

不同积分变分原理的统一

依据定量因果原理的数学表示，统一地导出了Lagrange量中含坐标关于时间一阶、二阶导数 的积分型的Hamilton原理、Voss原理、Hlder原理和Maupertuis-Lagrange原理等，给出了 这些原理的本质联系和统一描述.得出f₀=0并不是通常的保持Euler-Lagrange方 程不 变的结果，而是满足定量因果原理的结果.还得出Lagrange量的所有的积分型变分原理等价 地对应于两类满足定量因果原理的不变形式.同时发现所有积分型变分原理的运动方程都是E uler-Lagrange 方程，但不同条件的变分原理所对应的不同群Ｇ作用下的守恒量是不同 的.从而可对过去众多零散的积分型变分原理有一个系统和深入的理解，并使这些变分原理 自然地成为定量因果原理的推论. 关键词： 变分原理 因果原理 运动方程 对称性     

奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性

研究奇异系统Hamilton正则方程的形式不变性即Mei对称性，给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明结果的应用. 关键词： 奇异系统 Hamilton正则方程 约束 对称性 守恒量     

规范变换对求解Schrdinger方程的应用

在大部分量子力学书中都讨论了规范交换理论．并且强调指出量子力学体系的某种守恒律和规范变换的对称性具有密切的关系．考虑体系规范变换的对称性，可以使问题大大简化，并且能够得到一些有用的结果．本文利用规范变换来求解含时的 Ｓｃｈｒｏｄｉｎｇｅｒ方程．     

三质点Toda晶格微分方程的积分

三质点Toda晶格的微分方程是一个Hamilton系统.研究用Noether理论和Poisson理论求其积分. 关键词： Toda晶格 Hamilton系统 Noether理论 Poisson理论     

电位移矢量D与自由电荷激发场E_0关系的讨论

本文从场量的积分方程出发阐明：在均匀各向同性 电介质充满存在电场的全部空间，或介质表面为等位面的条件下，是满足 Ｄ＝ε０Ｅ０的，并对其物理意义做了说明．     

Path integral approach for superintegrable potentials on spaces of nonconstant curvature: I. Darboux spaces <Emphasis Type="Italic">D</Emphasis><Subscript>I</Subscript> and <Emphasis Type="Italic">D</Emphasis><Subscript>II</Subscript>

In this paper, the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of nonconstant curvature: these spaces are Darboux spaces D _I and D _II. On D _I, there are three, and on D _II four such potentials. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D _I in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. The text was submitted by the authors in English.     

非含Cu氧化物超导体的超导电性机制

基于单占据ａ_ｉσ表象和电荷涨落机制，应用简并微扰理论推导了非含ｃｕ氧化物Ｂａ_1-x·Ｋ_xＢｉＯ₃的双带Ｈｕｂｂａｒｄ模型有效哈密顿量．考虑到坐标空间两个相反自旋空穴的次近邻格位配对，得到了格林函数运动方程和超导方程．合理解释了超交换作用和跳跃能对次近邻配对的作用，并且超导窗是由于坐标空间Ｃｏｏｐｅｒ配对的结果． 关键词：     

The region of existence of the three-dimensional continuum bipolaron

The ranges of ?^*/?_∞ and of the electron-phonon coupling constant in which the three-dimensional bipolaron exists are determined. The limits of these ranges correspond to the emergence of the first bound state of two polarons. The criteria for the first bound state to arise are found by solving an integral equation, which corresponds to a Schrödinger equation describing internal vibrations of a bipolaron. The Hamiltonian describing these vibrations is separated from the complete Hamiltonian of the electron-phonon system by using the Bogoliubov-Tyablikov method of canonical transformations of coordinates.     

Role of surface integrals in the Hamiltonian formulation of general relativity

It is shown that if the phase space of general relativity is defined so as to contain the trajectories representing solutions of the equations of motion then, for asymptotically flat spaces, the Hamiltonian does not vanish but its value is given rather by a nonzero surface integral. If the deformations of the surface on which the state is defined are restricted so that the surface moves asymptotically parallel to itself in the time direction, then the surface integral gives directly the energy of the system, prior to fixing the coordinates or solving the constraints. Under more general conditions (when asymptotic Poincaré transformations are allowed) the surface integrals giving the total momentum and angular momentum also contribute to the Hamiltonian. These quantities are also identified without reference to a particular fixation of the coordinates. When coordinate conditions are imposed the associated reduced Hamiltonian is unambiguously obtained by introducing the solutions of the constraints into the surface integral giving the numerical value of the unreduced Hamiltonian. In the present treatment there are therefore no divergences that cease to be divergences after coordinate conditions are imposed. The procedure of reduction of the Hamiltonian is explicity carried out for two cases: (a) Maximal slicing, (b) ADM coordinate conditions.A Hamiltonian formalism which is manifestly covariant under Poincaré transformations at infinity is presented. In such a formalism the ten independent variables describing the asymptotic location of the surface are introduced, together with corresponding conjugate momenta, as new canonical variables in the same footing with the g_ij, π^ij. In this context one may fix the coordinates in the “interior” but still leave open the possibility of making asymptotic Poincaré transformations. In that case all ten generators of the Poincaré group are obtained by inserting the solution of the constraints into corresponding surface integrals.     

A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Theory of fragmentation dynamics in nucleus-nucleus collisions

The fragmentation of a nuclear system is described by a dynamical coordinate, the fragmentation coordinate η=A₁?A₂/A₁+A₂ The total Hamiltonian describing a binary heavy ion encounter includes a part H(R, α,η) which describes the fragmentation and its coupling to other degrees of freedom. It is a collective Hamiltonian which is calculated from the microscopic Asymmetric Two-Center Shell Model (ATCSM). The properties of this Hamiltonian are extensively discussed and methods for its solution are described. Formulae for cross sections of specific nuclear fragmentations including fusion are derived.     

Integrabilty of the BFKL dynamics and Pomeron trajectories in a thermostat

We consider scattering amplitudes in QCD at high energies $\sqrt s $ and fixed momentum transfers $q = \sqrt { - t} $ with a non-zero temperature T in the t-channel. In the s-channel the temperature leads to a compactification of the impact parameter plane. We find that the thermal BFKL Hamiltonian in the leading logarithmic approximation proceeds to have the property of the holomorphic separability. Moreover, there exists an integral of motion allowing one to construct the Pomeron wave function for arbitrary T in the coordinate and momentum representations. The holomorphic Hamiltonian for n-reggeized gluons at T ≠ 0 in the multicolour limit N _c → ∞ turns out to be equal to the local Hamiltonian for an integrable Heisenberg spin model. Further, the two-gluon Baxter function coincides with the corresponding wave function in the momentum representation. We calculate the spectrum of the Pomeron Regge trajectories at a finite temperature with taking into account the QCD running coupling. The important effect of the t-channel temperature is the appearence of a confining potential between gluons.     

TheA n /(1) face models

Presented here is the construction of solvable two-dimensional lattice models associated with the affine Lie algebraA _n ^/(1) and an arbitrary pair of Young diagrams. The models comprise two kinds of fluctuation variables; one lives on the sites and takes on dominant integral weights of a fixed level, the other lives on edges and assumes the weights of the representations ofsl(n+1, C) specified by Young diagrams. The Boltzmann weights are elliptic solutions of the Yang-Baxter equation. Some conjectures on the one point functions are put forth.     

Center of mass integral in canonical general relativity

For a two-surface B tending to an infinite-radius round sphere at spatial infinity, we consider the Brown-York boundary integral H_B belonging to the energy sector of the gravitational Hamiltonian. Assuming that the lapse function behaves as N∼1 in the limit, we find agreement between H_B and the total Arnowitt-Deser-Misner energy, an agreement first noted by Braden, Brown, Whiting, and York. However, we argue that the Arnowitt-Deser-Misner mass-aspect differs from a gauge invariant mass-aspect by a pure divergence on the unit sphere. We also examine the boundary integral H_B corresponding to the Hamiltonian generator of an asymptotic boost, in which case the lapse N∼x^k grows like one of the asymptotically Cartesian coordinate functions. Such a two-surface integral defines the kth component of the center of mass for (the initial data belonging to) a Cauchy surface Σ bounded by B. In the large-radius limit, we find agreement between H_B and an integral introduced by Beig and Murchadha as an improvement upon the center-of-mass integral first written down by Regge and Teitelboim. Although both H_B and the Beig- Murchadha integral are naively divergent, they are in fact finite modulo the Hamiltonian constraint. Furthermore, we examine the relationship between H_B and a certain two-surface integral which is linear in the spacetime Riemann curvature tensor. Similar integrals featuring the curvature appear in works by Ashtekar and Hansen, Penrose, Goldberg, and Hayward. Within the canonical 3+1 formalism, we define gravitational energy and center of mass as certain moments of Riemann curvature.     

N-soliton quantum scattering in the sine-Gordon theory

The quantum treatment of soliton scattering in the sine-Gordon model, using the path integral collective coordinate method is generalized to N solitons. The solitions. The first quantum correction to the phase shift of N-soliton scattering is equal to the zero-point energy of an effective multi-soliton Hamiltonian. The energies of the oscillators of this Hamiltonian are shown to be equal to the stability angles of a complete set of solutions of the Schrödinger equation for small fluctuations around a classical N-soliton. Consequently, calculating the fluctuations and their stability angles by the inverse scattering method, we obtain the energies of the oscillators. The first quantum correction to the phase shift (the O(1) part in a development in powers of γ) is evaluated by summing the stability angles. This result is in agreement with the “exact” scattering amplitude conjectured by Faddeev, Kulish and Korepin.