  The geometrical picture of gauge theories must be enlarged when a gauge
potential ceases to behave like a connection, as it does in electroweak
interactions. When the gauge group has dimension four, the vector space
isomorphism between spacetime and the gauge algebra is realized by a
tetrad-like field. The object measuring the deviation from a strict bundle
structure has the formal behavior of a spacetime connection, of which the
deformed gauge field-strength is the torsion. A generalized derivative emerges
in terms of which the two Bianchi identities are formally recovered. Effects of
gravitational type turn up. The dynamical equations obtained correspond to a
broken gauge model on a curved spacetime.
