Gauge-natural forms of Chern-Weil type (Q1345021)

In the beginning the author gives a geometric construction, transforming a connection on a principal bundle \(P(M,G)\) into an \(E\)-valued differential form, if \(E\) denotes the vector bundle associated with \(P\) by means of a linear representation of \(G\) in a vector space. This allows him to generalize the ordinary real-valued Chern-Weil differential forms to \(E\)-valued ones. It is then proved that every gauge-natural operator, transforming connections on \(P\) into \(E\)-valued forms, is defined by an appropriate equivariant polynomial map from the Lie algebra of \(G\) into the standard fibre of \(E\). The proof of the previous result is based on a generalization of Utiyama's theorem, on gauge-natural Lagrangians, within the present setting.