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The Yang–Mills Equation

  • Gerd RudolphEmail author
  • Matthias Schmidt
Chapter
  • 3k Downloads
Part of the Theoretical and Mathematical Physics book series (TMP)

Abstract

We present the geometric model of pure gauge theory, including the basics concerning the structure of the classical configuration space, and derive the Yang-Mills equation from the classical action functional. Next, we study the theory of instantons in a systematic way: we present the BPST-instanton family and the famous ADHM-construction, including a partial proof that this construction yields all instanton solutions. Moreover, we study the instanton moduli space. Finally, we present the classical stability analysis of the Yang-Mills equation as developed by Bourguignon and Lawson and discuss non-minimal solutions.

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsUniversity of LeipzigLeipzigGermany

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