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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Does the return flux result in the Aharonov-Bohm scattering amplitude?

Jun Liang

Published Aug 15, 1985• 9 citations
Publisher

Abstract

Introducing a new Aharonov-Bohm-type scattering model, the ambiguity of the incoming wave function is avoided and the single-valued wave function is uniquely determined by proper boundary conditions. In our model, however, the return flux plays an important role in deriving the Aharonov-Bohm scattering amplitude.
DOI
10.1103/physrevd.32.1014

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arXiv:hep-th/9610219•International Journal of Modern Physics A•Feb 20, 1998•3 citations
The scattering problem under the influence of the Aharonov–Bohm (AB) potential is reconsidered. By solving the Lippmann–Schwinger (LS) equation we obtain the wave function of the scattering state in this system. In spite of working with a plane wave as an incident wave we obtain the same wave function as was given by Aharonov and Bohm. Another method to solve the scattering problem is given by making use of a modified version of Gordon’s idea, which was invented to consider the scattering by the Coulomb potential. These two methods give the same result, which guarantees the validity of taking an incident plane wave as usual to make an analysis of this scattering problem. The scattering problem by a solenoid of finite radius is also discussed, and we find that the vector potential of the solenoid affects the charged particles, even when the magnitude of the flux is an odd integer as well as a noninteger. It is shown that the unitarity of the S matrix holds provided that a plane wave is taken to be an incident one.
We discuss the unitarity relation of the Aharonov–Bohm scattering amplitude with the hope that it distinguishes between the differing treatment which employ different incident waves. We find that the original Aharonov–Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other land, the amplitude obtained by Ruijsenaars who uses plane wave as incident wave also satisfies the unitarity relation but in an unusual way.