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Preface

Published online by Cambridge University Press:  15 December 2009

Steven Carlip
Affiliation:
University of California, Davis
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Summary

Interest in (2+1)-dimensional gravity – general relativity in two spatial dimensions plus time – dates back at least to 1963, when Staruszkiewicz first showed that point particles in a (2+1)-dimensional spacetime could be given a simple and elegant geometrical description. Over the next 20 years occasional papers on classical and quantum mechanical aspects appeared, but until recently the subject remained largely a curiosity.

Two discoveries changed this. In 1984, Deser, Jackiw, and 't Hooft began a systematic investigation of the behavior of classical and quantum mechanical point sources in (2+1)-dimensional gravity, showing that such systems exhibit interesting behavior both as toy models for (3+1)-dimensional quantum gravity and as realistic models of cosmic strings. Interest in this work was heightened when Gott showed that spacetimes containing a pair of cosmic strings could admit closed timelike curves; (2+1)-dimensional gravity quickly became a testing ground for issues of causality violation. Then in 1988, Witten showed that (2+1)-dimensional general relativity could be rewritten as a Chern–Simons theory, permitting exact computations of topology-changing amplitudes. The Chern–Simons formulation had been recognized a few years earlier by Achúcarro and Townsend, but Witten's rediscovery came at a time that the quantum mechanical treatment of Chern–Simons theory was advancing rapidly, and connections were quickly made to topological field theories, three-manifold topology, quantum groups, and other areas under active investigation.

Together, the work on point particle scattering and the Chern–Simons formulation ignited an explosion of new research.

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Publisher: Cambridge University Press
Print publication year: 1998

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  • Preface
  • Steven Carlip, University of California, Davis
  • Book: Quantum Gravity in 2+1 Dimensions
  • Online publication: 15 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511564192.001
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  • Preface
  • Steven Carlip, University of California, Davis
  • Book: Quantum Gravity in 2+1 Dimensions
  • Online publication: 15 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511564192.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preface
  • Steven Carlip, University of California, Davis
  • Book: Quantum Gravity in 2+1 Dimensions
  • Online publication: 15 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511564192.001
Available formats
×