Quantization of gauge fields through fibre bundle multiconnectivity |
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Authors: | Ouassim Ben Khalifa Claude Gauthier |
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Institution: | (1) Département de Mathématiques et de Statistique, Université de Moncton, Moncton, N.-B., E1A 3E9, Canada |
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Abstract: | 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.
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Keywords: | Gauge theory discrete group multiconnectivity quantization fibre bundle |
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