Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,786 comments
1,470 users with positive rep
820 active unimported users
More ...

  Gentle introduction to fibre bundles and gauge connections

+ 5 like - 0 dislike
5996 views

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.

asked Feb 6, 2013 in Resources and References by Dilaton (6,240 points) [ revision history ]
recategorized Apr 24, 2014 by dimension10
I have noted that this question is related and looks similar, but the answers do not contain what I am looking for.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Dilaton

5 Answers

+ 3 like - 0 dislike
A good math book about (mostly vector) bundles and connections is

C.H. Taubes, Differential geometry. Bundles, connections, metrics and curvature ( http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780199605880.001.0001/acprof-9780199605880 ).
answered Jun 15, 2015 by just-learning (95 points) [ no revision ]
+ 2 like - 0 dislike

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"

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user K.Ghosh
answered Feb 6, 2013 by K.Ghosh (0 points) [ no revision ]
Thanks for this hint, I hope you do not mind that I inserted a link to the book.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Dilaton
+ 2 like - 0 dislike

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.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Neal
answered Feb 6, 2013 by Neal (0 points) [ no revision ]
+ 2 like - 0 dislike

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

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user nonlinearism
answered Feb 6, 2013 by nonlinearism (0 points) [ no revision ]
Thanks, this looks nice too.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Dilaton
+ 1 like - 0 dislike

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.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Doldrums
answered Oct 29, 2013 by Doldrums (0 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar\varnothing$sicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...