自对偶引力的局部对称性与约束

LOCAL SYMMETRIES AND CONSTRAINTS IN SELF DUAL GRAVITY

在Ａｓｈｔｅｋａｒ形式下，广义相对论的相空间被嵌入到复ＳＵ（２）ＹａｎｇＭｉｌｓ理论的相空间里．将一般场论中分析局部对称性与约束的方法推广到复的场论，从自对偶Ｐａｌａｔｉｎｉ形式的位形空间构造出Ａｓｈｔｅｋａｒ形式的相空间，进而讨论了位形空间上的局部对称性与相空间上的约束的关系．

In Ashtekar's formalism, the phase space of general relativity is imbedded into the phase space of complex SU (2) Yang Mills theory. In this paper, the approach of analyzing local symmetries and constraints in ordinary feild theories is generalized to the complex field theory, the phase space of the Ashtekar formalism is constructed from the configuration space of the self dual Palatini formalism, and the relationship hetween local symmetries of the configuration space and constraints on the phase space is then discussed.