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Journal
2007 | 5 | 2 | 151-164
Article title

Quantization of gauge fields through fibre bundle multiconnectivity

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Languages of publication
EN
Abstracts
EN
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.
Publisher
Journal
Year
Volume
5
Issue
2
Pages
151-164
Physical description
Dates
published
1 - 6 - 2007
online
12 - 2 - 2007
References
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  • [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.
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  • [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.
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  • [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
bwmeta1.element.-psjd-doi-10_2478_s11534-007-0002-0
Identifiers
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