The Axiomatic Geometric Approach to Bundles

Eberhard Zeidler
Additional contact information
Eberhard Zeidler: Max Planck Institute for Mathematics in the Sciences

Chapter 17 in Quantum Field Theory III: Gauge Theory, 2011, pp 875-903 from Springer

Abstract: Abstract Our strategy is to define the notion of vector bundles and principal bundles in an invariant way by only using geometric properties of manifolds. In order to prove further geometric properties of these manifolds (e.g., curvature or parallel transport), we use the fact that, by definition, these properties do not depend on the choice of local bundle coordinates. Therefore, we can pass to special bundle coordinates. This is the situation of product bundles considered in Sects. 15.1 through 15.3. This way, the general results are immediate consequences of our special results about product bundles. In this chapter, we tacitly assume that all the objects are smooth, that is, they are described by smooth functions with respect to local coordinates.

Keywords: Gauge Theory; Gauge Group; Vector Bundle; Tangent Vector; Parallel Transport (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-22421-8_18

Ordering information: This item can be ordered from
http://www.springer.com/9783642224218

DOI: 10.1007/978-3-642-22421-8_18

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().