Quantization of gauge fields through fibre bundle multiconnectivity

• Authors: Ouassim Khalifa , Claude Gauthier
• 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.

Keywords

EN

Gauge theory; discrete group; multiconnectivity; quantization; fibre bundle

Discipline

• 11.15.-q: Gauge field theories
• 12.10.-g: Unified field theories and models(see also 04.50.-h Higher-dimensional gravity and other theories of gravity—in general relativity and gravitation, 11.25.Mj Compactification and four-dimensional models)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2007
• Volume: 5
• Issue: 2
• Pages: 151-164

Dates

published

1 - 6 - 2007

online

12 - 2 - 2007

Contributors

author

Ouassim Khalifa

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

author

Claude Gauthier

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

References

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Identifiers

DOI

10.2478/s11534-007-0002-0