Abstract
We develop a gauge theory or theory of bundles and connections on them at the level of braids and tangles. Extending recent algebraic work, we provide now a fully diagrammatic treatment of principal bundles, a theory of global gauge transformations, associated braided fiber bundles and covariant derivatives on them. We describe the local structure for a concrete ℤ3-graded or 'anyonic' realization of the theory.
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