Metric space as a model of spacetime: Classical theory and quantization

  • C. J. Isham
  • Yu. A. Kubyshin
  • P. Renteln
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 383)


An approach to describing the dynamics of spacetime, in which the basic variable is the distance function (metric) or a metric space, is considered. We study the set M (X) of all metrics on a set X and show that, for a finite set X, almost all such metrics can be obtained by embedding X into a vector space V and then varying the norm on V. A quantum theory of norms on V is constructed. A simple illustrative model which can produce a change in metric topology is presented.


Quantum Gravity Smooth Manifold Vector Space Versus Canonical Quantization Spacetime Foam 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • C. J. Isham
    • 1
  • Yu. A. Kubyshin
    • 2
  • P. Renteln
    • 3
  1. 1.Blackett LaboratoryImperial CollegeLondonUK
  2. 2.CFNUniversidade de LisboaLisboa CodexPortugal
  3. 3.Joint Science DepartmentThe Claremont CollegesClaremontUSA

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