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[Untitled]

Authors :
M. Socolovsky
M. A. Aguilar
Source :
International Journal of Theoretical Physics. 41:839-860
Publication Year :
2002
Publisher :
Springer Science and Business Media LLC, 2002.

Abstract

The validity of Green's theorem, and hence of Stokes' theorem, when the involved vector field is differentiable but not continuously differentiable, is crucial for a theoretical explanation of the Aharonov–Bohm (A-B) effect; we review this theorem. We describe the principal bundle in which the A-B effect occurs, and give the geometrical description of the relevant connection. We study the set of gauge equivalence classes of flat connections on a product bundle with abelian structural group, and show that this set has a canonical group structure, which is isomorphic to a quotient of cohomology groups. We apply this result to the A-B bundle and calculate the holonomy groups of all flat connections.

Details

ISSN :
00207748
Volume :
41
Database :
OpenAIRE
Journal :
International Journal of Theoretical Physics
Accession number :
edsair.doi...........c28561729f5142cec83b35b715ce768b
Full Text :
https://doi.org/10.1023/a:1015780806734