标题： 微分同胚不变场论的完整量化 显示英文标题

标题： Complete quantization of a diffeomorphism invariant field theory

摘要： 为了测试广义相对论的规范量子化方案，我们引入了一个复化Ashtekar引力实部的简化模型，该模型捕捉了全理论的重要特性。 虽然它并不对应于爱因斯坦引力的一个子集，但它具有优势，即可以通过简化的相空间方法或沿着代数量子化方案的路线，完全且明确地进行规范量子化程序。 这个模型与经常研究的圆柱对称波密切相关。 与其他在新变量下被研究的模型不同，这里的简化的相空间是无限维的，而标量约束在动量中是真正的双线性的。 无限数量的Dirac可观测量可以用原始相空间变量的简洁和显式形式表示。 它们如预期的那样是非局部的，并自然形成一个可数基数的集合。 显示英文摘要

摘要： In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not correspond to a subset of Einstein's gravity it has the advantage that the programme of canonical quantization can be carried out completely and explicitly, both, via the reduced phase space approach or along the lines of the algebraic quantization programme. This model stands in close correspondence to the frequently treated cylindrically symmetric waves. In contrast to other models that have been looked at up to now in terms of the new variables the reduced phase space is infinite dimensional while the scalar constraint is genuinely bilinear in the momenta. The infinite number of Dirac observables can be expressed in compact and explicit form in terms of the original phase space variables. They turn out, as expected, to be non-local and form naturally a set of countable cardinality.