自对偶引力理论中相空间变量的实数化研究  

On the Real Variables of the Phase Space in the Self-Dual Gravitational Theory

作　　者：吴亚波[1] 

机构地区：[1]大连理工大学应用数学系

出　　处：《大连大学学报》1999年第2期10-14,18,共6页Journal of Dalian University

基　　金：国家自然科学基金!19475005;辽宁省自然科学基金!9706211049

摘　　要：本文针对自对假引力理论中对场变量强加的“实条件”问题展开讨论．通过引入一个参数化的正则变换，将Hilbert-Palatini引力理论中的SO（3）ADM相空间司哈密顿约束方程变换成阿西特卡相空间参数化的约束方程利用参数的不同取值，我们不仅能得到罗仑兹时空中的阿西特卡引力理论和欧几里德时空中的实自对偶引力理论，而且还能给出其它一些新结果．尤其是能将罗仑兹时空中阿西特卡相空间的正则变量实数化，从而取消了对场变量强加的“实条件”In this paper the problem of the real conditions forced on field variables in the self-dual gravitational theory is discussed. By introducing a parametric canonical transformation, Hamiltonian constraint equation in SO(3)ADM phase space is transformed into the parametric form in Ashtekar phase spase. Moreover, by use of the different parameter values, we can not only obtain Ashtekar theory in Lorentzian spacetime and the real self-dual gravitational theory in Euclidean spacetime, but also give other new results. Especially, we can get real canonical variables in Ashtekar phase space, and therefore, the real conditions forced on the field variables can be canceled.

关 键 词：自对偶引力理论 相空间变量 实数化 正则变换 约束方程 引力场 

分 类 号：O314[理学—一般力学与力学基础]