ANNALS OF PHYSICS 146, 1-34 (1983) The Aharonov-Bohm Effect and Scattering Theory

The Aharonov-Bohm effect is studied from the viewpoint of scattering theory. A scattering experiment is proposed that could distinguish between two different dynamics that have been considered in the literature. The behavior of the S-matrices under gauge transformations is established and an anomalous cluster property is found. 1. INTR~DLJCTI~N More than 20 years after the work of Aharonov and Bohm [l] and the subsequent experiments, the effect named after these authors (but first predicted by Ehrenberg and Siday [2]) is still a hotly debated issue. (An extensive bibliography covering the period 1959-1971 can be found in [3].) The main experimental findings concern the shift in the interference pattern due to two coherent electron beams under the influence of a tiny solenoid or magnetized whisker placed between the two beams [4,5]. The results themselves are uncontested, but the theoretical description and interpretation of [ I] have been challenged by several authors [3, 6-111. A recent and particularly loud criticism is due to Bocchieri, Loinger and Siragusa [ 12-17, 531. The main objections raised by the latter authors concern the continuity of the wav