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Connections
Why is it interesting?
Our interest in connections was originally motivated (in Chapter 0) by the suggestion that such a structure would provide the unique path lifting procedure whereby one might keep track of the evolution of a particle’s internal state (e.g., phase) as it traverses the field established by some other particle (e.g., the electromagnetic field of a magnetic monopole). Topology, Geometry and Gauge Fields: Foundations by Naber
Layman
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
Student
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
Researcher
The motto in this section is: the higher the level of abstraction, the better.
Examples
- Example1
- Example2:
FAQ
History
The historical evolution of our definition of the curvature form from more familiar notions of curvature (e.g., for curves and surfaces) is not easily related in a few words. Happily, Volume II of [Sp2] is a leisurely and entertaining account of this very story which we heartily recommend to the reader in search of motivation. Topology, Geometry and Gauge Fields: Foundations by Naber
[Sp2] is Spivak, M., A Comprehensive Introduction to Differential Geometry, Volumes I–V, Publish or Perish, Inc., Boston, 1979.
advanced_tools/connections.1510734828.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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