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Fibre Bundles

20.10.2014 - Felix J Rudolph

Many important concepts and theories in physics can be interpreted in terms of the geometry of fibre bundles. Maxwell's theory of electromagnetism, 
Yang-Mills theories and also Einstein's theory of gravity are all essentially theories of connections on a bundle. Also the non-trivial topologies of the 
Moebius strip and the Dirac monopole can be formulated in terms of fibre bundles.

In this Journal Club I talked about the basics of fibre bundles, their definition and formulation. We learned about vector bundles, line bundles, tangent 
bundles and principle bundles and introduced some structures like connections.

I demonstrated the basic concepts in three examples, going up in complexity. The simplest one is the Moebius strip which everyone is familiar with. 
Then we covered the Dirac monopole which I used in some recent work. IIn the end, we looked at the Yang-Mills instantons which have some 
interesting structures.

Most of this Journal Club is based on Sections 4 and 5 in the review by Eguchi, Gilkey and Hanson. The monograph by Goeckeler and Schuecker 
was recommended by David Berman and covers the same material in Chapters 9 and 10. The references can be found at the end of the PDF.

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