Higher-Dimensional Algebra and Planck-Scale Physics

Details Higher-Dimensional Algebra and Planck-Scale Physics Higher-Dimensional Algebra and Planck-Scale Physics

1999-02-04

arxiv.org/abs/gr-qc/9902017v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages LaTeX, 6 encapsulated Postscript figures

Scientific paper

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'.

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