- #1
Geezer
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Okay, so I was reviewing the Aharonov-Bohm effect online, and found some related discussion on Dirac Monopoles. Let me quote a bit:
I don't understand a lick of it. What kind of math do I need to take to understand this stuff?
-Geez
In order to combine this local system into a -principal bundle, on the -coordinate over must be related to the -coordinate over by , with integer . This explains the appearance of Dirac's string singularity when the are extended to , and the fact that it can be removed by a gauge transformation which requires Dirac's quantization condition. Thus, the trivial bundle admits no monopole (charge -monopole). The existence of a monopole indicates non-triviality of a corresponding principal bundle. The monopole of charge is the connection in the Hopf fibration , while the monopole of charge with corresponds to the -bundle over with the lens space as a total space ( is viewed inside as a subgroup of th roots of the unit matrix)
I don't understand a lick of it. What kind of math do I need to take to understand this stuff?
-Geez