TG-Equivariance of Connections and Gauge Transformations
  We consider the notion of a connection on a principal bundle $P(M,G)$ from the point of view of the action of the tangential group $TG$. This leads to a new definition of a connection and allows to interpret gauge transformations as effect of the $TG$ action. 
H. M. Bosselmann, N.A. Papadopoulos