Geometry of Yang-Mills Fields (Publications of the Scuola Normale Superiore / Crm)

by Michael F. Atiyah

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These Lecture Notes are an expanded version of the Fermi Lectures I gave at Scuola Normale Superiore in Pisa, the Loeb Lectures at Harvard and the Whittemore Lectures at Yale, in 1978. In all cases I was addressing a mixed audience of mathematicians and physicists and the presentation had to be tailored accordingly. Throughout, I presented the mathematical material in a somewhat unorthodox order, following a pattern which I felt would relate the new techniques to familiar ground for physicists. The main new results presented in the lectures, namely the construction of all multi-istanton solutions of Yang-Mills fields, is the culmination of several years of fruitful interaction between many physicists and mathematicians.The major breakthrough came with the observation by Ward that the complex methods developed by Penrose in his 'twistor programme' were ideally suited to the study of the Yang-Mills equations. The instanton problem was then seen to be equivalent to a problem in complex analysis and to one in algebraic geometry. Using the powerful methods of modern algebraic geometry it was not long before the problem was finally solved.
  • ISBN10 8876423036
  • ISBN13 9788876423031
  • Publish Date 1 October 1979
  • Publish Status Active
  • Out of Print 13 January 2023
  • Publish Country IT
  • Publisher Birkhauser Verlag AG
  • Imprint Scuola Normale Superiore
  • Format Paperback
  • Pages 98
  • Language English