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  "body": "\n## Summary\n\nA connection on a [[principal bundle|8E37E74XVP]] with structure group $G$ is an [[Ehresmann connection|TD6VEP3SCE]] that is invariant under the action of $G$.\nIt is usually given by a connection form, a $1$-form on the total space with values in the Lie algebra of $G$.\nA principal connection induces connections on all associated vector bundles, so it is the universal form of a connection.\nIn physics these connections are the gauge fields, and their curvature is the field strength.\n\n## Explanations\n\n### L1 human\n\nA principal bundle has, above each point of the base, a copy of a symmetry group whose origin has not been fixed.\nA connection tells how to move from one fibre to a nearby one, and it must respect the symmetry.\nThe connection form does this by reading off, from each tangent vector, how fast it moves along the group direction.\nFor the trivial bundle $M \\times G$ there is a flat choice: moving in $M$ while staying at the same group element.\n",
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