Fibre bundles for describing gauge invariance

[limarodessa]

Hello all !

My question:

Does fibre bundles are necessary for describing gauge invariance in electromagnetic case? Or fibre bundles uses only for describing gauge invariance in cases of weak, electroweak and strong interactions?

Thanks

 

[tom.stoer]

They are not necessary in the sense that you can perfectly understand gauge invariance (for abelian as well for non-abelian symmetries) for many practical purposes w/o referring to fibre bundles.

But the underlying mathematical structures are fibre bundles, and there are some topics where the related tools and insights are useful or necessary. In addition the modern literature especially regarding topological aspects of gauge theories (partially) uses fibre bundles.

But of course there are aspects of the standard model which are accessable w/o ever referring to fibre bundles (Feynman, Weinberg, 't Hooft and many others were awarded nobel prizes - and I guess at that time they never discussed fibre bundles)