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Abstract: This talk will be the conclusion of my previous talk, but I will give a self-contained presentation. I will define U(n)-connections (as covariant derivatives on n-component vector functions) and their curvature. The norm-squared of the curvature is then the Lagrangian density whose integral is the famous "Yang-Mills functional". I will calculate the Euler-Lagrange equations for the U(1)-connections and show the relationship with Maxwell's system of equations for the electromagnetic field.
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