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The Aharonov-Bohm effect and scattering theory. (English) Zbl 0554.47003
The scattering of electrons off a cylinder inside which there is a current-carrying solenoid is considered. There are two different viewpoints on the description of the excluded magnetic fields and they lead to different hamiltonians. The corresponding S-matrices and scattering cross sections are found and it is shown that they differ considerably for \(R/\lambda \to 0\) \((R=cylinder\) radius, \(\lambda =de\) Broglie wave length of the electron), hence an experiment could serve to verify one description and falsify the other one. The idealized situation \(R=0\) is also studied. The S-matrices are explicitely obtained, it is shown that the results are invariant under a large class of gauge transformations and an anomalous long-range behaviour of the wave and scattering operator is pointed out.
Reviewer: V.Georgescu

MSC:
47A40 Scattering theory of linear operators
81U20 \(S\)-matrix theory, etc. in quantum theory
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