International Journal of Theoretical Physics

, Volume 35, Issue 6, pp 1037–1062 | Cite as

Principle of event symmetry

  • Philip E. Gibbs
Article

Abstract

To accommodate topology change, the symmetry of space-time must be extended from the diffeomorphism group of a manifold to the symmetric group acting on the discrete set of space-time events. This is the principle ofevent-symmetric space-time. I investigate a number of physical toy models with this symmetry to gain some insight into the likely nature of event-symmetric space-time. In the more advanced models the symmetric group is embedded into larger structures such as matrix groups which provide scope to unify space-time symmetry with the internal gauge symmetries of particle physics. I also suggest that the symmetric group of space-time could be related to the symmetric group acting to exchange identical particles, implying a unification of space-time and matter. I end with a definition of a new type of loop symmetry which is important in event-symmetric superstring theory.

Keywords

Manifold Gauge Symmetry Particle Physic Symmetric Group Large Structure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alvarez-Gaume, L., and Manes, J. L. (1991). Supermatrix models,Modern Physics Letters A,6, 2039–2050.ADSMathSciNetGoogle Scholar
  2. Ambjorn, J., Durhuus, B., and Jonsson, T. (1991). Three dimensional simplicial gravity and generalised matrix models,Modern Physics Letters A,6, 1133.ADSMathSciNetGoogle Scholar
  3. Antonsen, F. (1994). Random graphs as a model for pregeometry,International Journal of Theoretical Physics,33, 1189.MATHMathSciNetGoogle Scholar
  4. Aspinwall, P. S., Greene, B. R., and Morrison, D. R. (1994). Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory,Nuclear Physics B,416, 414–480 [hep-th/9309097].CrossRefADSMathSciNetGoogle Scholar
  5. Balachandran, A. P., Bimonte, G., Marmo, G., and Simoni, A. (1995). Topology change and quantum physics,Nuclear Physics B,446, 299–314 [gr-qc/9503046].CrossRefADSMathSciNetGoogle Scholar
  6. Bekenstein, J. D. (1994). Entropy bounds and black hole remnants,Physical Review D,49, 1912–1921 [gr-qc/9307035].CrossRefADSMathSciNetGoogle Scholar
  7. Bennet, D. L., Brene, N., and Nielsen, H. B. (1987). Random dynamics,Physica Scripta T,15, 158.ADSGoogle Scholar
  8. Borcherds, R. (1995). Private communication.Google Scholar
  9. Boulatov, D. V. (1992). A model of three dimensional lattice gravity,Modern Physics Letters A,7, 1629–1646 [hep-th/9202074].ADSMATHMathSciNetGoogle Scholar
  10. Boulatov, D. V., Kazakov, V. A., Kostov, I. K., and Migdal, A. A. (1986). Analytical and numerical study of the model of dynamically triangulated random surfaces,Nuclear Physics B,275, 641.CrossRefADSMathSciNetGoogle Scholar
  11. Bouwknegt, P., and Schoutens, K. (1993).W symmetry in conformal field theory,Physics Reports,223, 183–276 [hep-th/9210010].CrossRefADSMathSciNetGoogle Scholar
  12. Dadic, I., and Pisk, K. (1979). Dynamics of discrete structure,International Journal of Theoretical Physics,18, 345–358.Google Scholar
  13. Dimakis, A., Muller-Hoissen, F., and Vanderseypen, F. (1995). Discrete differential manifolds and dynamics of networks,Journal of Mathematical Physics,36, 3771–3791 [hep-th/9408114].CrossRefADSMathSciNetGoogle Scholar
  14. Evako, A. V. (1994). Dimension on discrete spaces,International Journal of Theoretical Physics,33, 1553–1568 [gr-qc/9402035].CrossRefMATHMathSciNetGoogle Scholar
  15. Finkelstein, D. (1982). Quantum sets and Clifford algebras,International Journal of Theoretical Physics,21, 489.ADSMATHMathSciNetGoogle Scholar
  16. Finkelstein, D., and Gibbs, M. J. (1993). Quantum relativity,International Journal of Theoretical Physics,32, 1801.CrossRefMathSciNetGoogle Scholar
  17. Fuchs, J. (1992).Affine Lie Algebras and Quantum Groups, Cambridge University Press, Cambridge.Google Scholar
  18. Fukuma, M., Hosono, S., and Kawai, H. (1994). Lattice topological field theory in two dimensions,Communications in Mathematical Physics,161, 157–176 [hep-th/9212154].CrossRefMathSciNetGoogle Scholar
  19. Garay, L. J. (1994). Quantum gravity and minimum length,International Journal of Modern Physics A,10, 145–166 [gr-qc/9403008].ADSGoogle Scholar
  20. Gebert, R. W. (1993). Introduction to vertex algebras, Borcherds algebras and the monster Lie algebra,International Journal of Modern Physics A,8, 5441–5504 [hep-th/9308151].ADSMATHMathSciNetGoogle Scholar
  21. Gibbs, P. E. (1994a). Models on event-symmetric space-time, PEG-01-94 [hep-th/9404139].Google Scholar
  22. Gibbs, P. E. (1994b). Event symmetric open string field theory, PEG-02-94 [hep-th/9405172].Google Scholar
  23. Gibbs, P. E. (1994c). Strings and loops in event-symmetric space-time, PEG-03-94 [hepth/9407136].Google Scholar
  24. Gibbs, P. E. (1995a). Symmetry in the topological phase of string theory, PEG-05-95 [hepth/9504149].Google Scholar
  25. Gibbs, P. E. (1995b). Event-symmetric physics, PEG-04-95 [hep-th/9505089].Google Scholar
  26. Gibbs, P. E. (1995c). The small scale structure of space-time: A bibliographical review, PEG-06-95 [hep-th/9506171],International Journal of Theoretical Physics, submitted.Google Scholar
  27. Gilbert, G., and Perry, M. J. (1991). Random supermatrices and critical behaviour,Nuclear Physics B,364, 734–748.CrossRefADSMathSciNetGoogle Scholar
  28. Gross, D. J. (1988). High energy symmetries of string theory,Physical Review Letters,60, 1229.ADSMathSciNetGoogle Scholar
  29. Hull, C. M., and Townsend, P. K. (1995). Unity of superstring dualities,Nuclear Physics B,438, 109.CrossRefADSMathSciNetGoogle Scholar
  30. Kaku, M. (1988). Geometric derivation of string field theory from first principles,Physical Review D,38, 3052.ADSMathSciNetGoogle Scholar
  31. Kaku, M. (1990). Deriving the four string interaction from geometric string field theory,International Journal of Modern Physics A,5, 659.ADSMathSciNetGoogle Scholar
  32. Kaneko, T., and Sugawara, H. (1983). On the structure of space, time and field,Progress of Theoretical Physics,69, 262.ADSMathSciNetGoogle Scholar
  33. Kaplunovsky, V., and Weinstein, M. (1985). Space-time: arena or illusion?Physical Review D,31, 1879.CrossRefADSMathSciNetGoogle Scholar
  34. Kazakov, V. A. (1989). The appearance of matter fields from quantum fluctuations of 2-D gravity,Modern Physics Letters A,4, 2125.ADSMathSciNetGoogle Scholar
  35. Klebanov, I., and Susskind, L. (1988). Continuum strings from discrete field theories,Nuclear Physics B,309, 175.CrossRefADSMathSciNetGoogle Scholar
  36. Kostov, I. K. (1995). Field theory of open and closed strings with discrete target space,Physics Letters B,344, 135–142 [hep-th/9410164].CrossRefADSMathSciNetGoogle Scholar
  37. Orland, P. (1993). The space-time manifold as a critical solid, BCUNY-HEP-93-1 [hep-th/9304004].Google Scholar
  38. Pressley, A., and Segal, G. (1988).Loop Groups, Oxford University Press, Oxford.Google Scholar
  39. Requardt, M. (1995). Discrete mathematics and physics on the Planck-scale, GOET-TP-101-95 [hep-th/9504118].Google Scholar
  40. Rossi, P., and Tan, C.-I. (1995). Simplicial chiral models,Physical Review D,51, 7159–7161 [hep-th/9412182].CrossRefADSMathSciNetGoogle Scholar
  41. Sasakura, N. (1991). Tensor model for gravity and orientability of manifold,Modern Physics Letters A,6, 2613–2624.ADSMATHMathSciNetGoogle Scholar
  42. Shen, X. (1992).W-Infinity and string-theory,International Journal of Modern Physics A,7, 6953–6994 [hep-th/9202072].ADSMATHGoogle Scholar
  43. Smith, F. D. (1994).SU(3) ×SU(2) ×U(1), Higgs, and gravity from spin(0,8) Clifford algebraCL(0,8), THEP-94-1 [hep-th/9402003].Google Scholar
  44. T'Hooft, G. (1974). A two-dimensional model for mesons,Nuclear Physics B,75, 461.ADSMathSciNetGoogle Scholar
  45. Thorn, C. B. (1991). Reformulating string theory with the 1/N expansion, UFIFT-HEP-91-23, Invited talk given at 1st Sakharov Conference on Physics, Moscow, 1991 [hep-th/9405069].Google Scholar
  46. Wheeler, J. A. (1957). On the nature of quantum geometrodynamics,Annals of Physics,2, 604.CrossRefMATHMathSciNetGoogle Scholar
  47. Wheeler, J. A. (1994).At Home in the Universe, American Institute of Physics Press, New York.Google Scholar
  48. Wilson, K. G. (1974). Confinement of quarks,Physical Review D,10, 2445.ADSGoogle Scholar
  49. Witten, E. (1993). Space-time transitions in string theory, IASSNS-HEP-93/36 [hep-th/9306104].Google Scholar
  50. Yost, S. A. (1992). Supermatrix models,International Journal of Modern Physics A,7, 6105–6120 [hep-th/9111033].ADSMATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Philip E. Gibbs
    • 1
  1. 1.EurocontrolBretigny Sur Orge Cedex 2France

Personalised recommendations