标题： 复数引力的真实表述和真实引力的复数表述 显示英文标题

标题： Real Formulations of Complex Gravity and a Complex Formulation of Real Gravity

摘要： 两种在Yang-Mills相空间上的规范和微分同胚不变理论被研究。 它们基于李代数$so(1,3)$和$\widetilde{so(3)}$-- 也就是$so(3)$的环代数。 尽管这些理论是显然实的，但它们都可以重新表述，以表明它们分别描述复数引力和无限多个复数引力的副本。 给出了与实数引力的联系。 对于这些理论，传统Ashtekar形式中的实数条件由正常的约束类似项表示。 显示英文摘要

摘要： Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space are studied. They are based on the Lie-algebras $so(1,3)$ and $\widetilde{so(3)}$ -- the loop-algebra of $so(3)$. Although the theories are manifestly real, they can both be reformulated to show that they describe complex gravity and an infinite number of copies of complex gravity, respectively. The connection to real gravity is given. For these theories, the reality conditions in the conventional Ashtekar formulation are represented by normal constraint-like terms.