Gentle introduction to fibre bundles and gauge connections

Question

To better understand papers like this for example, which makes heavy use of fibre bundles and gauge connections to represent gauge fields, I am looking for a nice introduction to this topic.

The only thing I have read so far is the corresponding chapter 15 of Roger Penrose's "Road to Reality".

I do not want to read a whole book, I am rather thinking about an appropriate introductory paper, lecture notes, or a tutorial.

I have noted that this question is related and looks similar, but the answers do not contain what I am looking for. — Dilaton, Feb 06 '13 at 10:04

score 5 · Answer 1 · edited Feb 06 '13 at 11:48

5

for fiber bundles,you may look into novikov's modern geometry part 2. it gives nice explanation and a good place to do learn some "real geometry"

edited Feb 06 '13 at 11:48

Ittay Weiss

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answered Feb 06 '13 at 10:02

Koushik

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Thanks for this hint, I hope you do not mind that I inserted a link to the book. – Dilaton Feb 06 '13 at 11:44

score 5 · Accepted Answer · answered Feb 06 '13 at 12:19

You can find the definition of a fiber bundle and some examples on pp 376-379 of Hatcher's online book Algebraic Topology. You might also consult "Fiber Bundles," chapter 4 of Lecture Notes in Algebraic Topology, by Davis-Kirk. A fast introduction to connections and curvature can be found here. In the case of surfaces, chapter 3 of these lecture notes might be useful to you.

score 2 · Answer 3 · edited Feb 06 '13 at 16:18

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For a 'physicsy' viewpoint, checkout "Geometry of Physics" by Frankel.

edited Feb 06 '13 at 16:18

Dilaton

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answered Feb 06 '13 at 15:56

nonlinearism

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Thanks, this looks nice too. – Dilaton Feb 06 '13 at 16:13

score 2 · Answer 4 · 2013-10-29T14:01:00.683

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I do not know what are gauge connections. However for connections on bundles, a "lecture note" reference is J.-L. Koszul's Lectures on Fibre Bundles and Differential Geometry.

edited Oct 29 '13 at 14:01

answered Oct 29 '13 at 11:31

The term "gauge connection" is not correct. Physicists use the term "gauge field" to denote a connection on a principal bundle. In fact, they usually denote by "gauge field" the local pull-back to the base of the connection one-form. A gauge transformation would be nothing but a right action of the Lie group of the bundle (assuming the transition functions act on the left). – Bilateral Mar 25 '15 at 15:33

Gentle introduction to fibre bundles and gauge connections

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