Summary
We show that the so-called alternative interpretation of the Aharonov-Bohm effect meets with certain difficulties when being applied to the scattering on the solenoids surrounded by various topologically nonequivalent potential barriers. We give the counter-example showing that an effect of unaccessible fields may be observed in the simply-connected space too.
Riassunto
Si mostra che la cosiddetta interpretazione alternativa dell’effetto di Aharonov-Bohm incontra certe difficoltà quando si applica allo scattering sui solenoidi circondati da varie barriere di potenziale topologicamente non equivalenti. Si dà il controesempio mostrando che un effetto dei campi non accessibili può essere osservato anche nello spazio semplicemente connesso.
Реэюме
Мы покаэываем, что так наэываемая альтернативная интерпретация зффекта Аарнова-Бома встречает некоторые трудности в том случае, когда применяется к рассеянию на соленоидах, которые окружены раэличными топологически незквивалентными потенциальными барьерами. Мы приводим контр-пример, покаэываюший, что влияние недоступных полей может наблюдаться также в просто-свяэном пространстве.
Similar content being viewed by others
References
G. N. Afanasiev:JINR, P2-87-154 (Dubna, 1987).
G. N. Afanasiev:JINR, P4-87-106; P4-87-107 (Dubna, 1987) (accepted for publication inJ. Phys. A);G. N. Afanasiev:J. Comput. Phys.,69, 196 (1987).
S. M. Roy:Phys. Rev. Lett.,44, 111 (1980);D. Home andS. Sengupta:Am. J. Phys.,51, 942 (1983).
F. Strocchi andA. S. Wightman:J. Math. Phys. (N. Y.),15, 2198 (1974);G. Casati andI. Guarneri:Phys. Rev. Lett.,42, 1579 (1979);P. Bocchieri, A. Loinger andG. Siragusa:Nuovo Cimento A,51, 1 (1979);W. C. Henneberger:Lett. Math. Phys.,11, 309 (1986);G. A. Goldin, R. Menikoff andD. H. Sharp:J. Math. Phys. (N. Y.),22, 1664 (1981).
J. Q. Liang andX. X. Ding:Phys. Lett. A,119, 325 (1987);A. Loinger:Fundamental Aspects of Quantum Theory (Como, Italy, 1985), p. 321.
E. Merzbacher:Am. J. Phys.,30, 237 (1962);M. Kretschmar:Z. Phys.,187, 73 (1965);W. C. Henneberger:J. Math. Phys. (N. Y.),22, 116 (1981);M. Bawin andA. Burnel:J. Phys. A,18, 2123 (1985).
P. Bocchieri andA. Loinger:Nuovo Cimento A,47, 475 (1978);Lett. Nuovo Cimento,39, 148 (1984);J. Q. Liang:Nuovo Cimento B,92, 167 (1986);A. Loinger:Riv. Nuovo Cimento,10, 1 (1987);M. Peshkin:Phys. Rep.,80, 375 (1981);S. N. M. Ruijsenaars:Ann. Phys. (N. Y.),146, 1 (1983);S. Olariu andI. I. Popescu:Rev. Mod. Phys.,57, 339 (1985);E. Comay:Phys. Lett. A,120, 196 (1987);P. Bocchieri:Fundamental Aspects of Quantum Theory (Como, Italy, 1985), p. 325.
S. M. Roy andV. Singh:Nuovo Cimento A,79, 391 (1986).
C. N. Yang: inProceedings of the International Symposium on Foundations of Quantum Mechanics, edited byS. Kamefuchi (Tokyo, Jap. Phys. Soc., 1984), p. 5;Y. Aharonov: inProceedings of the International Symposium on Foundations of Quantum Mechanics, edited byS. Kamefuchi (Tokyo, Jap. Phys. Soc., 1984), p. 10;N. Gauthier andP. Rochon:J. Math. Phys. (N. Y.),26, 2128 (1985).
C. N. Yang andT. T. Wu:Phys. Rev. D,12, 3845 (1975).
P. M. Morse andH. Feshbach:Methods of Theoretical Physic, Vol. 2 (McGraw Hill, New York, N.Y., 1953).
H. J. Rothe:Nuovo Cimento A,62, 54 (1981);C. Philippidis, D. Bohm andR. D. Kaye:Nuovo Cimento B,71, 75 (1982);S. Olariu andI. I. Popescu:Phys. Rev. D,33, 1701 (1986).
J. A. Mignaco andC. A. Novaes:Lett. Nuovo Cimento,26, 453 (1981).
G. N. Afanasiev:JINR Rapid Commun., No. 6, 17 (1985).
H. J. Lipkin andM. Peshkin:Phys. Lett. B,118, 385 (1982);D. H. Kobe andJ. Q. Liang:Phys. Lett. A,118, 475 (1986);W. C. Henneberger andP. Huguenin:Helv. Phys. Acta,54, 444 (1981);A. Aharonov, C. K. Au, E. C. Lerner andJ. Q. Liang:Phys. Rev. D,29, 2396 (1984);B. Nagel:Phys. Rev. D,32, 3328 (1985);R. A. Brown:J. Phys. A,18, 2497 (1985);R. A. Brown:J. Phys. A,20, 3309 (1987).
A. Davidson:Anomalous space-time around the Aharonov-Bohm solenoid, Syracuse University Preprint SU-4228-346 (November 1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Afanasiev, G.N. On the alternative interpretation of the aharonov-bohm effect. Nuov Cim A 99, 647–660 (1988). https://doi.org/10.1007/BF02730630
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02730630