Summary
New arguments against the existence of the magnetic Aharonov-Bohm effect are given. In particular, the following points are emphasized: i) the time evolution of the expectation value of any observable depends only on the forces, and not on the potentials; ii) the choice of a Stokesian or a non-Stokesian vector potential is quite irrelevant; iii) if Bohm’s ideas were right, one could prove the existence of an Aharonov-Bohm effect also for aclassical charged continuum; iv) the recent analysis of the Marton experiment, due to Greenberger and Overhauser, proves that this experiment has nothing to do with the Aharonov-Bohm effect. Finally, in appendix A, the nonexistence of the electric Aharonov-Bohm effect is also proved. In appendix B, a nonrelativistic treatment of quantum electrodynamics, due to Pauli, which avoids completely the electromagnetic potentials, is briefly recalled.
Riassunto
Si sviluppano nuovi argomenti sull’inesistenza dell’effetto Aharonov-Bohm magnetico. Si sottolinea, in particolare, che 1) l’evoluzione temporale del valore di aspettazione di una qualunque osservabile dipende solo dalle forze e non dai potenziali elettromagnetici; 2) è del tutto irrilevante scegliere un potenziale vettore stokesiano o non stokesiano; 2′) del pari irrilevante è l’interpretazione (secondo l’analisi classica oppure secondo la teoria delle distribuzioni) dei potenziali non stokesiani; 3) se la concezione di Bohm fosse corretta, esisterebbe un effetto Aharonov-Bohm anche per un fluidoclassico elettricamente carico; 4) la recente analisi dell’esperimento di Marton, fatta da Greenberger e Overhauser, ha mostrato che tale esperimento non ha nulla a che fare con l’effetto Aharonov-Bohm, in contrasto con l’opinione sino ad oggi prevalsa. Infine, in una prima appendice, si dimostra l’inesistenza anche dell’effetto Aharonov-Bohm elettrico, e in una seconda appendice si richiama brevemente una trattazione, dovuta a Pauli, dell’elettrodinamica quantistica non relativistica, che evita l’introduzione dei potenziali elettromagnetici.
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Bocchieri, P., Loinger, A. & Siragusa, G. The role of the electromagnetic potentials in quantum mechanics. The marton experiment. Nuov Cim A 56, 55–72 (1980). https://doi.org/10.1007/BF02729980
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DOI: https://doi.org/10.1007/BF02729980