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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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The classifying space of a gauge group

Proof of (1): (a). Suppose $X$ and $Y$ are $G$-spaces, the action of $G$ on $X$ is free, and $X\to X/G$ is a principal bundle, then the space of $G$-equivariant maps $$ F(X,Y)^G $$ is the same th …
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