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I have studied the mathematical foundations of gauge theories - in particular, fiber bundles and connection 1-forms - and knowing that classical mechanics can be formulated with fiber bundles$^1$, I was wondering if the same holds for classical electrodynamics. If yes, I'd like to have some references.

$^1$ As far as I know, the main idea is that spacetime $M$ comes with a function $\pi\colon M\to A$ that assigns to each event a "time", modeled as a 1-dim. affine space $A$. In other words, we consider a bundle $(M,\pi,A)$.

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You could check out Baez and Munian's book Gauge Fields, Knots and Gravity, that IIRC has a whole chapter on classical EM as a U(1) fibre bundle.

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