Aharonov-Bohm Effect

In General > s.a. Aharonov-Casher; geometric phase; locality; topology in physics.
* Idea: The phase difference between wave functions of electrons going different ways around a line of magnetic dipoles.
* Significance: It shows that, even if B = 0, in some non simply connected region R, we cannot conclude that A = 0, because it is a connection, and this has physical effects beyond the presence of forces.
* Potential vs field: If one wants to obtain it as a local interaction of the electron current with something, then one has to use the vector potential A; But the effect can be explained as an interaction of the electron's magnetic field inside the solenoid with the other magnetic field, without using A's at all (Ó Raifeartaigh).
* Remark: It can be obtained for any theory of particles coupled to a connection, including gravity, with conical singularities.

References > s.a. charge [quantization]; non-commutative geometry; Sagnac Effect.
@ General: Bohm & Aharonov PR(57); Merzbacher AJP(62); Peshkin PRP(81); Peshkin & Tonomura 89; Holstein CP(95); Magni & Valz-Gris JMP(95); Adami & Teta LMP(98)qp/97 [Hamiltonians]; Dabrowski & Stovícek JMP(98) [ interaction]; Aharonov & Kaufherr PRL(04)qp; Tiwari qp/04 [and geometric phase]; Huérfano et al mp/07 [geometry].
@ Wave function: Alvarez PRA(96); Berry & Shelankov JPA(99); > s.a. representations in quantum mechanics.
@ Interpretation: Belot BJPS(98) [repercussions]; Blanco FP(99) [no classical interpretation]; Boyer FP(00), FP(00), FP(02); Costa de Beauregard FP(04) [and measurement of A]; Mattingly SHPMP(06) [gauge matters]; Caprez et al a0708 [macroscopic/classical test].
@ Experiments: Werner & Brill PRL(60); Boyer FPL(06) [and forces]; Caprez et al PRL(07) [showing absence of forces]; Byer FP(08).
@ Different particles and backgrounds: Horner & Goldhaber PRD(97) [for spin-1]; Alvarez JPA(99) [on a cone]; Spavieri PRL(99) [with electric dipole]; Sjöqvist AQC(04)qp/03 [molecular].
@ Gravitational analog: Bezerra JMP(89); Harris AJP(96) [for photons]; Tartaglia gq/00 [and lensing]; Barros et al MPLA(03); Marques & Bezerra PLA(03), MPLA(04).
@ Other topics: Holstein AJP(91) [variations]; Dowling et al PRL(99) [and similar phases]; Aguilar & Socolovsky IJTP(02) [and Green's theorem]; Furtado & Duarte PS(05) [dual]; Dragoman & Bogdan qp/05 [in momentum space]; Nesterov IJGMP(07) [and non-associative, path-dependent wave functions].

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