What are some good introductory texts to gauge theory? I have some basic differential geometry knowledge, but I don’t know any algebraic geometry.

Also, as a side question, what intuitively is a gauge field, and what are the Yang Mills equations saying?


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Two texts by Donaldson: Mathematical aspects of gauge theory, Mathematical uses of Gauge theory. I think the notion of Ehresmann connection (= gauge field, basically a field of horizontal subspaces) is fairly intuitive itself, and the Yang-Mills equations are the Euler-Lagrange equations associated to the Yang-Mills functional (which is a kind of energy functional, see here). So in a sense the solutions to the Y-M equations minimise energy.

  • $\begingroup$ These are definitely not introductory texts, as the OP is asking for. $\endgroup$ – Alex M. Mar 23 at 20:12
  • $\begingroup$ @AlexM. I think what is introductory is in the eye of the beholder. I knew nothing about gauge theory (just some basic differential geometry, which of course includes connections) when I started reading the first one, and I could follow it fairly well. They are notes written for graduate students. $\endgroup$ – Simpleton Mar 23 at 20:42

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