sl玻色子体系在U(2l+1)O(2l+2)过渡区的严格解

利用无穷维李代数方法得到了相互作用sl玻色子体系在U( 2l+ 1 ) O( 2l+ 2 )过渡区的能谱和波函数的严格解 .给出了该系统Bethe假定方程的数值解法 .     

sl玻色子体系在U（2l＋1）←→0（2l＋2）过渡区的严格解

利用无穷维李代数方法得到了相互作用sl玻色子体系在U（2l 1)←→0(2l 2)过渡区的能谱和波函数的严格解。给出了该系统Bethe假定方程的数值解法。     

sl玻色子体系在U(2l+1)→O(2l+2)过渡区的严格解

利用无穷维李代数方法得到了相互作用sl玻色子体系在U(2l+1)→O(2l+2)过渡区的能谱和波函数的严格解. 给出了该系统Bethe假定方程的数值解法.     

Clifford代数很值得在物理学中推广

Ｃｌｉｆｆｏｒｄ代数（几何代数或多重矢运算）比通常数学工具诸如矢量、张量、旋量及外微分形式有很多优越性。作为介绍性章这里选取刚体转动及放置参考系作为例子，以展示此种数学工具的优越性。中基本的几何代数运算及两个例子很容易在一般力学课程中讲授。     

SO(n)规范势的可分解理论

使用几何代数方法,研究了n维紧致黎曼流形上SO(n)规范势(自旋联络)的一般分解理论,建立了SO(n)规范场用球丛上单位矢量场n分解的一般表达式.由此,分别得到了U(1)规范场和U(2)规范场用单位矢量场n分解的一般形式.     

SU(2)规范场分解与Bose-Einstein凝聚体中的环流条件

利用SU(2)规范场的单位矢量场分解形式讨论了Bose-Einstein凝聚体中的环流条件.对于二分量Bose-Einstein凝聚,内部态的SU(2)对称性将导致一个拓扑环流条件,这是一个推广的Mer-min—Ho关系.     

Torus上一般复结构的Virasoro代数

我们讨论了torus上一般度规下,复结构的形式和相应的能量动量张量T(z),T(z);并在τ度规下,解torus上的玻色弦及其鬼的运动方程,得到了弦场和鬼场通解形式;最后我们给出了torus上一般复结构的Virasoro代数,并证明了不同复结构上的Virasoro代数相同.     

三维全息原子场作用失量用于苦味肽QSAR的研究

本文提出利用三维原子场相互作用矢量(3D-VAIF)对苦味二肽分子结构进行表征,并利用逐步回归(SMR)结合多元性性回归(MLR)建立苦味二肽定量构效关系模型,同时采用内外部双重验证的方法检验模型的稳定性。所建模型相关统计参量如下：复相关系数(Rcum2)、留一法（LOO）交互校验复相关系数(Rcv2)和外部样本校验复相关系数（Qext2）分别为0.983、0.934、0.876。结果表明,三维全息原子矢量法能较好的对苦味二肽结构进行表征,优于以往传统的氨基酸描述子。从而可以为新的强活性肽类药物的分子设计和改造提供了指导。     

Bessel光束的矢量分析及其能流密度的特征

通过比较自由空间Besssel光束标量解E(r,t)满足的方程和光场矢量E(r,t)与矢量势A(r,t)之间的关系表达式,利用Bessel的特点,合理构造了矢量势A(r,t)的具体形式,推导出电场量E(r,t)的磁场量B(r,t)各分量满足的具体形式。通过数值计算,给出电场E(r,t)在不同参数θ,φ下与径向坐标ρ之间的关系图线(图1,图2),发现由方程(6)描述的标量解仅是矢量场E(r,t)(方程15描述)在小θ下的近似。通过对能量传输特性的讨论,说明“超光速”的提法是不恰当的。     

利用具有非常规插入场的QCD求和规则计算核子张量荷

利用外张量场下的QCD求和规则计算了核子张量荷,其中核子插入场的核子流算符取最一般形式或称为非常规型,计算包括至维度8的项的贡献.详细分析了不同核子插入场及张量磁化率对计算核子张量荷求和规则的影响.计算表明,改变核子插入场及张量磁化率仍不能得到求和规则的稳定解,但如取最佳插入场的形式,对同位旋矢量和同位旋标量的求和规则解的稳定性有所改善.给出了在通常的对核子“QCD求和规则窗口”标度下核子张量荷的平均值.     

标架形式的简化旋量体系及其对杨振宁方程的应用

本文给出时空流形的一种简化的旋量描述形式。特别是证明了在Newman-Penrose方程中有六个多余的方程。作为对杨振宁引力场方程的应用,求得全部O型和一部分N型“纯粹空间”。     

Next‐to‐next‐to‐leading order post‐Newtonian linear‐in‐spin binary Hamiltonians

The next‐to‐next‐to‐leading order post‐Newtonian spin‐orbit and spin(1)‐spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt‐Deser‐Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter‐only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short‐range behavior of the integrands around the sources. The Hamiltonian of a test‐spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post‐Newtonian approximate) Poincaré algebra are applied. Along the way a self‐contained overview for the computation of the 3PN ADM point‐mass Hamiltonian is provided, too.     

一种Lorentz引力规范理论的正则形式

本文选择了一个特殊的、在任意座标变换下及局部Lorentz变换下不变的Lagrangian,着重讨论了在经典意义下的运动方程、给出了与Lagrangian相应的正则形式。 关键词：     

Classical effects from a factorized spinor representation of Maxwell's equations

It was demonstrated in earlier work that the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations (Sachs & Schwebel, 1962). The latter is a generalization of the usual formalism, in the sense that in addition to predicting all of the effects that are implied by the vector theory, it predicts additional observable effects that are out of the domain of prediction of the Maxwell formalism. The latter extra predictions were derived in previous publications (Sachs & Schwebel, 1961, 1963; Sachs, 1968a, b). In this paper, the spinor formalism is applied to effects that are expected to agree with the predictions of the standard formalism—the Coulomb force between point charges and the measured speed of a charged particle which moves in an electric potential. While there are no vector or tensor variables involved in this formalism, the results are found, as expected, to be in agreement with the conventional representation of electromagnetic theory. The analysis serves the role of demonstrating that in the appropriate limiting case, the factorized spinor formulation of electromagnetism does predict the explicit classical effects that are also predicted by Maxwell's field equations. The paper also presents a derivation of the general form of the solutions of the spinor field equations.     

Einstein-Dirac equations in suited tetrads

We write the Dirac and Einstein equations and the spinor Lagrangian in tetrads suited to the 1+3 formalism of general relativity.Dedicated to Achille Papapetrou on the occasion of his retirement.Stagiaire de recherches du Fonds National Belge de la Recherche Scientifique.     

A note on the solution of a spinor equation

An equation of spinor algebra, which is specified by two positive integers,M andN, is solved by relating it to the problem of integrating a two-dimensional Hamiltonian homogeneous polynomial system of ordinary differential equations, whose degree isN}-1. The case in whichN=1 reduces to a well-known result of spinor algebra. The caseM=N=4 is of relevance in the study of symmetry operators of Maxwell's equations on a curved space-time. It is also shown, using spinor notation, that the first integral for a general two-dimensional Hamiltonian system of ordinary differential equations (whether polynomial or analytic) is determinable in a purely algebraic manner, i.e., by using no integration.     

Field theoretic constraint formalism

The constraint formalism of classical mechanics is extended to field theories with gauge groups. Explicit examples of Klein-Gordon and Maxwell fields are presented. The symmetry properties of the Maxwell fields have the unexpcted feature in this formalism of forming a first-class algebra which is not Lie, a situation already encountered in the general theory of relativity.     

A new theory of elementary matter

This is the first of a series of articles that reviews and expands upon a new theory of elementary matter. This paper presents an exposition of the philosophical approach and its general implications. The ensuing explicit form of the mathematical expression of the theory and several applications in the atomic and elementary particle domains will be developed in the succeeding parts of this series.The theory is based on three axioms: the principle of general relativity, a generalized Mach principle, and a correspondence principle. The approach is basically a deterministic, relativistic field theory which fully incorporates the idea that any realistic physical system is in facta closed system, without separable parts. It is shown that the most primitive mathematical expression of this theory, following as anecessary consequence of its axioms, is in terms of a set of coupled nonlinear spinor field equations. Nevertheless, the exact formalism is constructed to asymptotically approach the quantum mechanical formalism for a many-particle system, in the limit of sufficiently small energy-momentum transfer among the components of the considered closed system. Thus, all of the mathematical predictions of nonrelativistic quantum mechanics are contained in this theory, as a mathematical approximation. However, predictions follow from the exact form of this theory (where energy-momentum transfer can be arbitrarily large) that are not contained in the quantum theory.     

A Spinor Approach to the SU(2) Clebsch-Gordan Coefficients *

We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two independent angular momentum vector operators. Utilizing the spinor algebra, we are able to develop a simple way for calculating the SU(2) Clebsch-Gordan (CG) coefficients. The explicit expression for the SU(2) CG coefficients is worked out, and some simple physical examples are presented to illustrate the spinor approach.     

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.