Abstract
Principal fibre bundles with connections provide geometrical models of gauge theories. Bundles allow for a global formulation of gauge theories: the potentials used in physics are pull-backs, by means of local sections, of the connection form defined on the total spaceP of the bundle. Given a representationP of the structure (gauge) groupG in a vector spaceV, one defines a (generalized) Higgs field α as a map fromP toV, equivariant under the action ofG inP. If the image of α is an orbitW ⊂V ofG, then a breaks (spontaneously) the symmetry: the isotropy (little) group ofw 0 eW is the “unbroken” groupH. The principal bundleP is then reduced to a subbundleQ with structure groupH. Gravitation corresponds to a linear connection, i.e. to a connection on the bundle of frames. This bundle has more structure than an abstract principal bundle: it is soldered to the base. Soldering results in the occurrence of torsion. The metric tensor is a Higgs field breaking the symmetry fromGL (4,R) to the Lorentz group.
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