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Pointless Spaces and Quantum Gravity

  • Robert W. Carroll
Part of the Mathematics and Its Applications book series (MAIA, volume 554)

Abstract

We sketch first a survey of some papers on the themes in the title (with embellishments and connections). Thus in Section 2 we consider ideas from [81, 283, 418, 486, 558, 577, 578, 579, 580, 621, 679, 680, 681, 682]. There are connections here to quantum mechanics (QM) on a discrete background as in [38, 39, 40, 70, 109, 221, 429, 430, 669, 670], to differential calculi on finite sets as in [29, 84, 109, 191, 191, 193, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204], fuzzy physics (cf. [429, 447] and references there), and to noncommutative geometry (NCG) (cf. [109, 155, 156, 280, 429, 447]). Some of the latter material will also be sketched. A basic driving impulse in all this is to understand QM and provide a properly (discrete) geometrical setting for QM, relativity, and classical mechanics (CM). In this direction there are many approaches to relating QM and CM behavior (see e.g. [109] and references there for a survey of some of this). To amplify this a little we will sketch some papers and results which are either more recent or have recently come to our attention; for example we cite [575, 390, 391, 392].

Keywords

Quantum Gravity Simplicial Complex Space Time Modular Group Hasse Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Robert W. Carroll
    • 1
  1. 1.Mathematics DepartmentUniversity of IllinoisUrbanaUSA

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