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28 March 2024
 
  » arxiv » gr-qc/9902017

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Higher-Dimensional Algebra and Planck-Scale Physics
John C. Baez ;
Date 4 Feb 1999
Subject General Relativity and Quantum Cosmology; Quantum Algebra; Category Theory | gr-qc hep-th math.CT math.QA
AbstractThis 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’.
Source arXiv, gr-qc/9902017
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