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Gauge theory in physics and mathematics refers to a field theory whose fields include principal bundles with connection.
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Prove that the holonomies along any two homotopic paths are the same if the curvature of the...
A possible answer would be to invoke Ambrose-Singer Holonomy theorem:
Theorem (Ambrose-Singer) Let $M$ be a (smooth) connected manifold, $E\to M$ a vector bundle over $M$, and $\nabla$ a connection o …