爱因斯坦引力场Arnowitt-Deser-Misner约束方程的两种推导方法

给出两种不同方法,分别导出爱因斯坦引力理论中著名的Arnowitt-Deser-Misner(ADM)约束方程.其一是在具有洛伦兹号差的时空中,构造一个单参数引力场作用量,由此导出单参数ADM约束方程.该参数取某特定值时对应的就是熟知的ADM约束方程.其二是将二重复函数理论运用于爱因斯坦引力场的哈密顿形式表述中,得到引力场ADM约束的二重化形式,从而也能将通常的ADM约束作为其特殊情况包含其中.此外,这两种方法还能统一地表述具有不同时空号差(洛伦兹号差和欧几里得号差)的洛伦兹引力理论和欧几里得引力理论 关键词： Arnowitt-Deser-Misner约束方程 哈密顿表述 时空号差 引力场作用量

TWO DIFFERENT METHODS OF DERIVING ARNO WITT-DESER MISNER CONSTRAINT EQUATIONS FOR EINSTEIN'S GRAVITATIONAL FIELDS

In this paper,two different methods are given,by which the famous Arnowitt-Deser-Misner (ADM) constraint equations for Einstein's gravitational fields can be derived.One method is to construct an action of gravitational fields with a parameter in the specetimes of Lorentzian sgnature.Thus,ADM constraints with a parameter can be obtained and the familiar ADM constraint equations can be naturally derived by adjusting the value of this parameter.The other is to apply the double complex function theory to gravitational fields in Hamiltonian formulation.Hence,the double constraints can be obtained,in which the well-known ADM constraint equations are included as a special case.In addition,the Lorentzian and Euclidean gravitational theory can be expressed in a unified way by use of these two different methods.