Czechoslovak Journal of Physics B

, Volume 29, Issue 1, pp 107–116 | Cite as

The geometry of gauge fields

  • A. Trautman


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 orbitWV ofG, then a breaks (spontaneously) the symmetry: the isotropy (little) group ofw0 εW 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.


Gauge Theory Isotropy Geometrical Model Fibre Bundle Gauge Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Academia, Publishing House of the Czechoslovak Academy of Sciences 1979

Authors and Affiliations

  • A. Trautman
    • 1
    • 2
  1. 1.Institute of Theoretical PhysicsWarsaw UniversityWarsawPoland
  2. 2.Polish Academy of SciencesPKiNWarsawPoland

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