5
$\begingroup$

I'm looking for a textbook or set of lecture notes on gauge theory for mathematicians that assumes only minimal background in physics. I'd prefer a text that uses more sophisticated mathematical concepts like principal bundles and connections, and categorical language whenever convenient.

$\endgroup$
  • $\begingroup$ Google is your friend... $\endgroup$ – Danu Oct 27 '15 at 21:16
  • 2
    $\begingroup$ Check out "Gauge fields, knots and gravity" by Baez and Munian. I think it strikes a nice balance between mathematical formalism and physical intuition. $\endgroup$ – Siva Oct 27 '15 at 21:16
  • $\begingroup$ You might see "Gauge Fields Knots and Gravity" by John Baez and Javier Munian. $\endgroup$ – Selene Routley Oct 27 '15 at 21:17
3
$\begingroup$

I have been writing something in this direction in section 1 of the book Differential cohomology in a Cohesive topos (pdf). Have a look, just focus on section 1 and ignore the remaining sections on first reading.

The survey-part is presently also appearing as a series on PhysicsForums. See at Higher prequantum geometry I, II, III, IV, V and Examples of Prequantum Field Theories I -- Gauge fields, II -- Higher gauge fields.

$\endgroup$
  • 2
    $\begingroup$ Please don't edit away the link to the pdf (dl.dropboxusercontent.com/u/12630719/dcct.pdf). It's more comprehensive. I will update the arXiv version soon. $\endgroup$ – Urs Schreiber Oct 27 '15 at 21:29
  • $\begingroup$ Thanks for the link! I just have a question: you say on page 4 that the curvature of a connection is a cocycle in nonabelian differential cohomology. I'm only familiar with the basics of the Chern-Weil homomorphism and characteristic classes, but it seems to me that the curvature is not in general a closed form. Is there some other sense in which the curvature form is a cocycle? $\endgroup$ – ಠ_ಠ Oct 28 '15 at 5:18
  • $\begingroup$ Which page 4 do you mean? Abelian curvatures are closed, otherwise the evaluation of the curvature in a characteristic polynomial is closed. $\endgroup$ – Urs Schreiber Oct 28 '15 at 8:50
  • 2
    $\begingroup$ The book looks amazing. $\endgroup$ – zzz Nov 8 '15 at 1:56
2
$\begingroup$

One less well-known but great reference are the classical field theory notes by Deligne and Freed in the '99 IAS lectures. Some good things about them

  • Very elegant treatment written for mathematicians
  • Begins with a nice discussion of ordinary classical mechanics using principal bundles and connections
  • Useful comments on supersymmetric gauge theories throughout.
$\endgroup$

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.