Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl


Preferences help
enabled [disable] Abstract
Number of results


2007 | 5 | 2 | 151-164

Article title

Quantization of gauge fields through fibre bundle multiconnectivity


Title variants

Languages of publication



A geometric model for the quantum nature of interaction fields is proposed. We utilize a trivial fibre bundle whose typical fibre has a multiconnectivity characterized by a discrete group Γ. By seeing Γ as a gauge group with global action on each fibre, we show that the corresponding field strength is non-zero only on the future part of the light cone whose vertex is at the interaction point. When the interaction is submitted to the symmetries of a Lie group G, we consider the gauge group G x Γ. The field strength of the gauge having this group includes a term expressing the quantization of the interaction field described by G. This geometric interpretation of quantization makes use of topological arguments similar to those applied to explain the Aharonov-Bohm effect. Two examples show how this interpretation applies to the cases of electromagnetic and gravitational fields.


  • Département de Mathématiques et de Statistique, Université de Moncton, Moncton, N.-B., E1A 3E9, Canada
  • Département de Mathématiques et de Statistique, Université de Moncton, Moncton, N.-B., E1A 3E9, Canada


  • [1] A. Pais: “Subtle is the Lord …”: The Science and Life of Albert Einstein, Oxford University Press, Oxford, 1982.
  • [2] O. Ben Khalifa: Quantification des champs de jauge via une multiconnexité des fibrés, Mémoire de maîtrise (M. Sc.), Université de Moncton, 2006.
  • [3] C. Gauthier and P. Gravel: “Jauge discontinue et particules dans un hyperespacetemps multiconnexe”, Nuovo Cimento A, Vol. 104, (1991), pp. 325–336.
  • [4] K. Moriyasu: An Elementary Primer for Gauge Theory, World Scientific, Singapore 1983.
  • [5] Y. Choquet-Bruhat, C. Dewitt-Morette and M. Dillard-Bleick: Analysis, Manifolds and Physics: Part I, North Holland, Amsterdam, 1982.
  • [6] Y. Choquet-Bruhat and C. Dewitt-Morette: Analysis, Manifolds and Physics: Part II, North Holland, Amsterdam, 1989.
  • [7] C. Gauthier and P. Gravel: “Le problème cosmologique dans les variétés de Kaluza-Klein multiconnexe”, Can. J. Phys., Vol. 68, (1990), pp. 385–387.
  • [8] M. Hamermesh: Group Theory, Addison-Wesley, Reading, MA, 1962.
  • [9] J.M. Nester: “Gravity, torsion and gauge theories”, In: H.C. Lee (Ed.): An Introduction to Kaluza-Klein Theories, World Scientific, Singapore, 1984.
  • [10] J.A. Wolf: Spaces of Constant Curvature, Publish or Perish, Boston, 1974.
  • [11] B. Doubrovine, S. Novikov and A. Fomenko: Géométrie contemporaine: méthodes et applications, Vol. 1, Mir, Moscow, 1982.
  • [12] C. Nash and S. Sen: Topology and Geometry for Physicists, Academic Press, London, 1983.
  • [13] C. Gauthier: “Quantum effects due to extra space multiconnectivity”, Nuovo Cimento A, Vol. 110, (1997), pp. 149–160.
  • [14] C. Gauthier: “Inertia and gravitation from extra space multiconnectivity: new prospects for the missing mass problem”, Gravitation & Cosmology, Vol. 5, (1999), pp. 203–214.
  • [15] C. Gauthier: “Space-time built-in particles and the exclusion principle from extra space multiconnectivity”, Nuovo Cimento B, Vol. 115, (2000), pp. 1167–1173.
  • [16] C. Gauthier: “Electromagnetism from extra space multiconnectivity”, Nuovo Cimento B, Vol. 116, (2001), pp. 1071–1081.

Document Type

Publication order reference


YADDA identifier

JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.