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- W65528195 abstract "The essence of the Aharonov-Bohm (AB) effect can be expressed mathematically by the fact that on a multiply connected space or space-time manifold there exist non-trivial connections with zero curvature. Put in more physical terms: we can have a potential which is not gauge equivalent to zero, although the field is zero everywhere in the accessible region. To specify the electromagnetic state - the “electromagnetic vacuum” - we then have to know, in the static case, the circulation ∮ Ā.dr̄ for closed paths not contractible to a point, or rather the corresponding phase factors exp(ie ∮Ā.dr̄/n̄). This means that for a manifold M the different possible vacua are indexed by the set Hom(π1 (M),U(1)) of all homomorphisms from the fundamental group π1 (M) of the manifold M to the gauge group U(l) of electro-magnetism. (See Asorey1 for the general case of an arbitrary gauge group G.)KeywordsFundamental GroupPartial WaveJump ConditionConnected SpaceZero CurvatureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W65528195 created "2016-06-24" @default.
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- W65528195 date "1986-01-01" @default.
- W65528195 modified "2023-10-02" @default.
- W65528195 title "Some Cases of the Aharonov-Bohm Effect: Electron Scattering on Magnetic Strings" @default.
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- W65528195 doi "https://doi.org/10.1007/978-1-4684-5221-1_40" @default.
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