拓扑与可微流形上的锥体与因果结构
摘要
presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or diffeomorphic abstraction from the standard null cone variety in R^{d+1}. Weak and strong local cone (LC) structures refer to the cone itself or a manifold thickening of the cone respectively. After introducing cone (C-)causality, a causal complement with reasonable duality properties can be defined. The most common causal concepts of space-times are generalized to the present topological setting. A new notion of precausality precludes inner boundaries within future/past cones. LC-structures, C-causality, a topological causal complement, and precausality may be useful tools in conformal and background independent formulations of (algebraic) quantum field theory and quantum gravity.
引用
@article{arxiv.gr-qc/9905106,
title = {Cones and causal structures on topological and differentiable manifolds},
author = {Martin Rainer},
journal= {arXiv preprint arXiv:gr-qc/9905106},
year = {2015}
}
备注
v3: 12 pages, latex+amssymb; compatibility conditions (2.5) and (3.2) with misprints corrected and improved argument