Abstract
The suggestion by Professor Bocchieri, Professor Loinger, and others1 that the Aharonov-Bohm effect (AB) is not part of quantum mechanics or that it can be removed from quantum mechanics without ruining the theory, is an important one for many reasons. One reason which has perhaps been too little emphasized is that removing AB scattering from the theory would remove the justification for Dirac’s charge quantization law
where e and g are the elementary units of electric and magnetic charge and n is an integer. In this discussion I shall summarize arguments that have been given in detail elsehwere2,3 to show why AB cannot in fact be removed from the theory except by spoiling the conservation and quantization of angular momentum. It is of course no coincidence that the most general proofs of Dirac’s charge quantization law also rely mainly on the quantization of angular momentum.4 I will not deal with that in this talk, but I will return briefly in an appendix to the relation between AB and Dirac’s original derivation of the charge quantization law from the now-familiar singular strings.
Keywords
- Angular Momentum
- Total Angular Momentum
- Centrifugal Barrier
- Inequivalent Representation
- Conventional Quantum Mechanic
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References
Representative statements of that point of view are given by Professor Bocchieri in the previous paper and by W. C. Henneberger in Phys. Rev. Lett. 52, 573 (1984), and in references therein. Henneberger’s “AB Scattering”, which he distinguishes from “AB Effect”, is included in my “AB”.
M. Peshkin, I. Talmi, and L. J. Tassie, Ann. Phys. 16, 177 (1961).
M. Peshkin, Phys. Rep. 80, 376 (1981).
J. Lipkin, W. I. Weisberger, and M. Peshkin, Ann. Phys. 53, 203 (1969), and references therein.
J. Tassie and M. Peshkin, Ann. Phys. 16, 177 (1961).
B. Nagel, this volume.
F. Wilczek, Phys. Rev. Lett. 48, 1144 (1982); and 49, 957 (1982).
P. A. M. Dirac, Proc. Roy. Soc. (London) A133, 60 (1931).
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© 1986 Plenum Press, New York
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Peshkin, M. (1986). Theories without AB effect Misrepresent the Dynamics of the Electromagnetic Field. In: Gorini, V., Frigerio, A. (eds) Fundamental Aspects of Quantum Theory. NATO ASI Series, vol 144. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5221-1_39
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DOI: https://doi.org/10.1007/978-1-4684-5221-1_39
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