Higher-Dimensional Algebra and Planck-Scale Physics
摘要
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local degrees of freedom propagating causally'. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensional spacetime. These are background-free quantum theories lacking local degrees of freedom, so they only display some of the features we seek. However, they suggest a deep link between the concepts of `space' and `state', and similarly those of `spacetime' and `process', which we argue is to be expected in any background-free quantum theory. We sketch how higher-dimensional algebra provides the mathematical tools to make this link precise. Finally, we comment on attempts to formulate a theory of quantum gravity in 4-dimensional spacetime using `spin networks' and `spin foams'.
引用
@article{arxiv.gr-qc/9902017,
title = {Higher-Dimensional Algebra and Planck-Scale Physics},
author = {John C. Baez},
journal= {arXiv preprint arXiv:gr-qc/9902017},
year = {2015}
}
备注
22 pages LaTeX, 6 encapsulated Postscript figures