5
$\begingroup$

I would like to learn gauge theory, starting from the simplest case. I have heard that I should start with electromagnetism, which is just the $U(1)$-gauge theory. All the references I know are written for physics students.

Being familiar with bundle theory, it would be nice if I can start with a short exposition that explains electromagnetism using the language of bundles, characteristic classes, curvatures, etc.. . Any relevant pointers are appreciated.

$\endgroup$
  • $\begingroup$ I like the lecture notes by José Figueroa-O'Farrill empg.maths.ed.ac.uk/Activities/GT $\endgroup$ – Appliqué Oct 9 '19 at 13:28
  • $\begingroup$ It seems to be useful! I will grok the first 5 lectures soon. $\endgroup$ – Student Oct 9 '19 at 14:54
4
$\begingroup$

John Baez wrote a book called Gauge Fields, Knots, and Gravity. I think it's probably what you're looking for.

$\endgroup$
  • $\begingroup$ His book is amazing indeed! But that book does not treat its readers as if they know bundle theory.. $\endgroup$ – Student Oct 9 '19 at 14:24
2
$\begingroup$

I think a comprehensive reference here would be Naber's Topology, Geometry and Gauge fields (Volume 1, Volume 2).

More specifically, Sections 0.2 of Volume 1 has a physical discussion of Maxwell's equations and Dirac monopoles, which is reformulated in differential-geometric language (i.e. principal bundles, connections, etc.) in Section 0.4.

$\endgroup$
1
$\begingroup$

The book "The Geometry of Physics: An Introduction", by Theodore Frankel is, despite its name, a fairly complete treatment.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.