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Okay, had said
The notion of field bundle captures only some aspects of the general notion of spaces of physical fields. See at field (physics) in the section The idea of field bundles and its problems for more.
I have expanded that now to
The notion of field bundle captures only some aspects of the general notion of spaces of physical fields. For instance the configurations of the B-field in general do not form sections of a fiber bundle (but of a fiber 2-bundle) and hence for instance the magnetic charge anomaly has no real description by field bundles. See at field (physics) in the section The idea of field bundles and its problems for more.
I have now considerable expanded the discussion at
More discussion about the issue that the “field bundle” is in general not a 1-bundle but a bundle in higher geometry is now taking place here.
I realize that I should have amplified this point long ago. Better late than never.
added a pointer to Schenkel 14 which makes more explicit the issue previously discussed in BDS 13.
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