 Associated vector bundle (source code)

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= Associated vector bundle
{title2=$E=P\times_\rho V$}

A linear representation $\rho:G\to GL(V)$ of a <principal bundle>'s structure group defines the quotient of $P\times V$ by $(p,v)\sim(pg,\rho(g)^{-1}v)$. It is a <vector bundle> over the same base. A <principal connection> induces <parallel transport> and a local <covariant derivative> $d+\rho_*(A)$ on its sections.

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