Principal Bundles and Gauge Theory

  • Corina KellerEmail author
Part of the BestMasters book series (BEST)


In many areas of theoretical physics we encounter fields defined on a spacetime M taking values in some other space F. For instance, presume F as a real finite-dimensional vector space, then : M → F is a vector field. More generally, we can consider a family of spaces {Fx}xϵM varying over the points on M, that is (x) ϵ Fx for each x ϵ M. A field is then understood as a section from the spacetime manifold into the bundle of spaces over M. This is exactly the idea encoded in the mathematical theory of fiber bundles. Namely, fiber bundles provide a tool to describe the global structure of physical fields.


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Copyright information

© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of ZurichZürichSwitzerland

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