International Journal of Theoretical Physics

, Volume 33, Issue 9, pp 1797–1809 | Cite as

Intrinsic algebraic characterization of space-time structure

  • Ulrich Bannier


Starting from a partially ordered set ofC*-algebras ℛ i representing algebras of observables of physical subsystems, we derive a topological Hausdorff space ℳ as a candidate for some generalized “space-time” with the help of which one can define a net\(O \to \mathcal{A}(O),O \subseteq \mathcal{M}\), of algebras. This opens a way to define a physical theory without an underlying metaphysical manifold, an aspect which may be relevant for the unification of general relativity and quantum field theory.


Manifold Field Theory General Relativity Elementary Particle Quantum Field Theory 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bannier, U. (1987). Allgemein kovariante algebraische Quantenfeldtheorie und Rekonstruktion von Raum-Zeit, Thesis, Hamburg, Germany.Google Scholar
  2. Bannier, U. (1988).Communications in Mathematical Physics,118, 162.Google Scholar
  3. Buchholz, D. (1974).Communications in Mathematical Physics,36, 287.Google Scholar
  4. Buchholz, D., D'Antoni, C., and Fredenhagen, K. (1987).Communications in Mathematical Physics,111, 123.Google Scholar
  5. Comfort, W. W., and Gordon, H. (1961).Proceedings of the American Mathematical Society,12, 327.Google Scholar
  6. Connes, A. (1982). Classification des facteurs, inProceedings of Symposia in Pure Mathematics, No. 38, Part 2, American Mathematical Society, Providence, Rhode Island.Google Scholar
  7. Dimock, J. (1980).Communications in Mathematical Physics,77, 219.Google Scholar
  8. Doplicher, S., and Longo, R. (1984).Inventiones Mathematicae,75, 493.Google Scholar
  9. Fredenhagen, K. (1992). On the general theory of quantized fields, inProceedings of the 10th Congress on Mathematical Physics, Leipzig 1991. K. Schmüdgen, ed., Springer-Verlag, Berlin.Google Scholar
  10. Haag, R. (1992).Local Quantum Physics;Fields, Particles, Algebras, Springer-Verlag, Berlin.Google Scholar
  11. Haag, R., and Kastler, D. (1964).Journal of Mathematical Physics,5, 848.Google Scholar
  12. Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge.Google Scholar
  13. Helly, E. (1923).Jahresbericht der Deutschen Mathematischen Vereinigung,32, 175.Google Scholar
  14. Landau, L. J. (1969).Communications in Mathematical Physics,13, 246.Google Scholar
  15. Radon, J. (1921).Mathematische Annalen,83, 113.Google Scholar
  16. Russell, B. (1976).Human Knowledge, Its Scope and Limits, George Allen and Unwin, London.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Ulrich Bannier
    • 1
  1. 1.Fachhochschule HamburgFachbereich MChHamburgGermany

Personalised recommendations