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1 2007

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Quantization of gauge fields through fibre bundle multiconnectivity

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Khalifa O. , Gauthier C.

Open Physics

2007

tom 5

nr 2

151-164

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.