A Brief Introduction to the Geometry of Gauge Fields

  • M. E. Mayer
  • A. Trautman
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 23/1981)


In view of the common background required for the understanding of the lectures of both authors, and in order to avoid unnecessary duplications, we have decided to present jointly this brief introduction to the language and properties of fiber bundles. By now the advantages of the fiber-bundle formulation of gauge field theories have led to a widespread acceptance of this language, and a number of reviews of the subject have appeared or are in course of publication. These, together with a number of standard textbooks are listed in the references to this introduction. Nevertheless, we felt that it would be convenient for the reader of these proceedings to have at his disposal a summary of the basic facts. We also tried to clarify a number of concepts and propose an acceptable terminology wherever a standard has not been established in the literature. This refers, in particular, to the terms gauge transformation, pure gauge transformation, and the related (infinite-dimensional) groups as well as to the concepts of extension, prolongation, restriction, and reduction of bundles, which are used with slightly varying meaning in different texts.


Gauge Theory Gauge Transformation Base Space Parallel Transport Principal Bundle 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • M. E. Mayer
    • 1
  • A. Trautman
    • 2
  1. 1.Dept. of PhysicsUniv. of CaliforniaIrvineUSA
  2. 2.Inst, of Theoretical PhysicsWarsaw Univ.WarsawPoland

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