标题： 谱几何和因果关系 显示英文标题

标题： Spectral Geometry and Causality

摘要： 对于量子引力理论的物理解释，有必要至少近似地恢复经典时空。 然而，量子引力可能最终通过提供类似于非交换几何中出现的谱数据来给出经典时空，而不是直接给出时空流形。 显示了一个全局双曲洛伦兹流形可以通过谱数据给出。 在谱几何的背景下观察到一种新现象：因果关系。 展示了利用谱数据的因果关系可以导致对洛伦兹流形的高度有效的描述，表明这种方法可能有用。 讨论了与自由量子场论的联系，以提供动机和物理解释。 假设必要的谱数据可以从具有广义量子力学基本结构的有效场论中通常获得：退相干泛函和历史选择。 显示英文摘要

摘要： For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of histories.