标题： 在Ashtekar变量中的Bianchi类型I和II的经典分析 显示英文标题

标题： Classical analysis of Bianchi types I and II in Ashtekar variables

摘要： 我们求解了在Ashtekar变量中表述的Bianchi I和II模型的复数Einstein方程。 然后我们求解现实条件，以实数共轭变量的形式对洛伦兹解的空间进行参数化。 在Ashtekar变量中，宇宙点粒子的动力学仅由一个弯曲的超度规控制——没有势能项。 在通常的度规形式中，粒子在平坦的超空间中碰到势能壁而反弹。 我们考虑在无势能的Ashtekar变量中对这种“反弹”可能的表征方式。 显示英文摘要

摘要： We solve the complex Einstein equations for Bianchi I and II models formulated in the Ashtekar variables. We then solve the reality conditions to obtain a parametrization of the space of Lorentzian solutions in terms of real canonically conjugate variables. In the Ashtekar variables, the dynamics of the universe point particle is governed by only a curved supermetric -- there is no potential term. In the usual metric formulation the particle bounces off a potential wall in flat superspace. We consider possible characterizations of this ``bounce'' in the potential-free Ashtekar variables.