规范场的正则量子化(Ⅲ)——引力场

本文在谐和条件下对引力场进行正则量子化.我们把引力场分解成横场和两种自对易场,研究了自对易场 X_μ的运动方程和自对易场对物理态之间的 S矩阵元的贡献,从而求得作用量中的规范补偿项.我们的结果和用轨道积分方法求得的相同,但是我们的方法可以克服 Gribov 规范不确定性的困难.     

量子几何与三旋

量子几何避开使用度规场，从而也不再引进所谓的背景度规，因此被称为是一种与背景无关的量子引力理论。但它以联络作为引力理论的基本变量，体现了将引力场视为规范场的物理思想。不仅如此，自旋联络作为引力理论的基本变量也为进一步研究这种耦合提供了舞台。传统的量子几何与超弦理论目前还是两个独立的理论，彼此之间唯一明显的相似之处是两者都使用了一维的几何概念作为理论基础。如果这两个理论都反映了物理世界某些本质特征，那么这种相似性也许就不是偶然的。三旋理论的研究已揭示出这种巧合背后的联系之谜。     

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.     

计算光在引力场中偏折的新方法

利用光的量子论,能量守恒及弱等效原理得出电磁波传播在几何近似下,光线在引力场中的偏转角和波矢的关系. 利用引力场中电磁波方程,在弱场近似下给出了一般的计算光线偏转角度的方法. 具体计算了Schwarzchild引力场中光线的偏折及Kerr-Newman引力场中光线的偏折. 关键词： 引力场 电磁波方程 能量守恒 弱场近似     

Anti-de Sitter时空中黑洞量子熵的发散结构

用“brick- wall”模型研究了Anti-de Sitter时空中起源于电磁和引力场的黑洞量子熵的发散结构, 结果表明量子熵由线性发散项和对数发散项构成. 如果平衡温度选为Hawking温度，固有截断替代坐标截断，则线性发散项可化为正比于事件视界面积的形式；而对数发散项不仅依赖于黑洞的特征，也依赖于场的自旋，由于此项的存在，自旋场的贡献不再与标量场的贡献成正比. 关键词： 发散结构 黑洞熵 AdS时空 电磁和引力场     

有关引力场高斯定理的探讨

基于牛顿的万有引力定律与静电场的库仑定律相似, 均满足平方反比定律, 对引力场的高斯定理进行 了探讨. 运用类比思想, 引入虚引力场强度, 提出了一种巧妙推导引力场高斯定理的新方法, 并用该方法推导出引力 场高斯定理的两种不同的表达形式, 同时对此做出了相关的分析. 理论表明该方法极其简单明了, 易于理解和掌握 运用, 具有一定的推广价值     

浅谈广义相对论的创立之三 引力场方程的确立与应用

简述了爱因斯坦建立的物质不存在时的引力场方程;介绍了爱因斯坦建立引力场方程的指导思想和方法;讨论了场方程的牛顿近似和水星近日点进动.     

SU(2)规范场的一系列“无源”解——静点磁荷系的SU(2)势及U(1)势

场与源这一对矛盾双方如何对立与统一是经典电磁场及引力场理论中议论纷云的一个根本问题.非Abel规范场的静无源解(应该说是无外源,但以场自身为源)提供了一个不含奇异点的、场与源互相制约构成自洽稳定的有机统一体的一个值得注意的例子(孤粒子).现有的这种解都是在无外源(实际上以场的奇异点——磁荷为源)的吴杨单位磁荷解([4]的情况a)的基础上加上径向“形状因子”得到的,因此只限于总磁荷为单位值(本文取Schwinger量子化值为磁荷单位)的静同步球对称情况.为了弄清楚更一般     

利用爱因斯坦转盘推求中心引力场中的光频红移--在普通物理教学中讲解等效原理的一种尝试

通过球对称引力场与爱因斯坦转盘上的惯性离心力场的对比，利用强等效原理导出光频的引力红移。     

一个引入规范场的方法

通常关于规范场的讨论是以波函数为基础进行的。用这个方法研究旋量粒子在引力场中的行为时,遇到了波函数在广义座标变换下为标量的著名问题。本文提出以代数结构,Lie代数或Jordan代数为基础讨论规范场的方法,引入了一个代数表示群的概念,把波函数的表示问题同表示群联系起来,表示群可以是整体的,也可以是定域的,分别与波函数的整体和定域交换相对应。按照这种方法研究规范场的问题发现,对于杨-Mills场这类涉及内部自由度的问题,给出的结果和常规的方法一致。借助于改变代数结构对旋量粒子引进引力,发现象Weyl所用的vierbein不再出现,波函数也不再表现为标量,而是以和Dirac理论相一致的方式进行变换。进一步的问题也作了讨论。     

Gauge fields and gravitational field equations

It is shown that the gravitational field equations in free space have a similar form to the free Yang-Mills field equations, where the group SL (2, C) replaces the group SU(2). The Ricci rotation coefficients take the role of the Yang-Mills like potentials, whereas the Riemann tensor takes the role of the gauge fields.     

Application of Lie Algebroid Structures to Unification of Einstein and Yang-Mills Field Equations

Yang-Mills field equations describe new forces in the context of Lie groups and principle bundles. It is of interest to know if the new forces and gravitation can be described in the context of algebroids. This work was intended as an attempt to answer last question. The basic idea is to construct Einstein field equation in an algebroid bundle associated to space-time manifold. This equation contains Einstein and Yang-Mills field equations simultaneously. Also this equation yields a new equation that can have interesting experimental results.     

Some global solutions of the Yang-Mills equations in Minkowski space

A class of global solutions of the Yang-Mills equations whose Cauchy data depend on a pair of arbitrary functions is constructed. The asymptotic propagation of the energy in space-time is studied. The same results are valid if the Yang-Mills field is coupled to a scalar field.Research supported in part by NSF Grants MCS 77-01340 and MCS 79-01965     

High-temperature limit of Landau-gauge Yang-Mills theory

The infrared properties of the high-temperature limit of Landau-gauge Yang-Mills theory are investigated. In a first step the high-temperature limit of the Dyson-Schwinger equations is taken. The resulting equations are identical to the Dyson-Schwinger equations of the dimensionally reduced theory, a three-dimensional Yang-Mills theory coupled to an effective adjoint Higgs field. These equations are solved analytically in the infrared and ultraviolet, and numerically for all Euclidean momenta. We find infrared enhancement for the Faddeev-Popov ghosts, infrared suppression for transverse gluons and a mass for the Higgs. These results imply long-range interactions and over-screening in the chromomagnetic sector of high-temperature Yang-Mills theory while in the chromoelectric sector only screening is observed.Received: 5 August 2004, Published online: 21 September 2004     

The interaction of classical Yang-Mills charges

Beginning with Khriplovich's formulation of the two point charge Yang-Mills problem, the gauge freedom is used to reduce by one the number of quantities entering the field equations. While a Coulomb solution is shown to exist for any orientation of the color charges, any solution which has a magnetic field present will have lower energy. When the field equations are solved for the simple charge configurations of parallel plates and cylindrical capacitors, one finds screening due to the vector potential. This screening is shown to be complete for any isolated charged plate or line charge. This result may be an indication that isolated charge cannot occur physically for the classical Yang-Mills theory.     

Gravitational instantons

The path-integral approach to quantum field theory assigns special importance to finite action Euclidean solutions of classical field equations. In Yang-Mills gauge theories, the instanton solutions of classical field equations with self-dual field strength have given rise to a new, nonperturbative treatment of the quantum field theory and its vacuum state. Since gravitation is also a species of gauge theory, one might think that similar phenomena would occur in gravity. The authors recently sought and found a new self-dual solution to Euclidean gravity which plays a role parallel to that of the Yang-Mills instanton. Gravitational instantons now promise to yield new insights into the nature of quantum gravity.This essay received the second award from the Gravity Research Foundation for the year 1979-Ed.     

Properties of exact solutions for a massive classical Yang-Mills field

Exact solutions for a massive Yang-Mills field are found and solutions of classical Wong equations and quantum Dirac equations are discussed for the field configurations obtained. A procedure for constructing constant fields is given and transition to solutions of the Yang-Mills equations in the case of a massless field is discussed.Translated from Izvestriya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 96–100, May, 1986.In conclusion, the authors express their gratitude to V. Ch. Zhukovskii and V. R. Khalilov for valuable remarks and discussions.     

On the linearization of source free gauge field equations

A scheme for linearizing the source free Yang-Mills field equations is given. An infinite parameter invariance group of the gauge field equations is discovered.