Comments on the Aharonov-Bohm Effect



Abstract Views
307

Downloads
249

Citations

Share

##plugins.themes.bootstrap3.article.sidebar##

Submitted Sep 4, 2022
Published Oct 20, 2022
10.24018/ejphysics.2022.4.5.209

Abstract viewed = 307 times

Table of Contents

##plugins.themes.bootstrap3.article.main##

In the original setting of the Aharonov-Bohm, the gauge invariant physical longitudinal mode of the vector potential, which is expressed by the gauge invariant physical current, gives the desired contribution to the Aharonov-Bohm effect. While the scalar mode of the vector potential, which changes under the gauge transformation so that it is the unphysical mode, give no contribution to the Aharonov-Bohm effect. Then Aharonov-Bohm effect really occurs by the physical longitudinal mode in the original Aharonov-Bohm’s setting. In the setting of Tonomura et al., where the magnet is shielded with the superconducting material, not only the magnetic field but also the longitudinal mode of the vector potential become massive by the Meissner effect. Then not only the magnetic field but also the physical longitudinal mode does not come out to the region where the electron travels. In such setting, only the scalar mode of the vector potential exists in the region where the electron travels, but there is no contribution to the Aharonov-Bohm effect from that mode.

Keywords: Aharonov-Bohm effect, non-simply connected region, physical longitudinal mode, Stokes’ theorem

References

  1. Aharonov Y, Bohm D. Significance of Electromagnetic Potentials in the Quantum Theory. Phys. Rev., 1959; 115: 485-491.
     Google Scholar
  2. Aharonov A, and Bohm D.Further Considerations on Electromagnetic Potentials in the Quantum Theory. Phys. Rev., 1961, 123: 1511-1524.
     Google Scholar
  3. Aharonov Y, Bohm D.Remarks on the Possibility of Quantum Electrodynamics without Potentials. Phys. Rev., 1962; 125: 2192-2193.
     Google Scholar
  4. Chambers RG, Shift of an Electron Interference Pattern by Enclosed Magnetic Flux. Phys. Rev. Lett., 1960; 5: 3-5.
     Google Scholar
  5. Fowler HA, Marton L, Simpson JA, Suddeth JA. Electron Interferometer Studies of Iron Whiskers. J. Appl. Phys., 1961; 32: 1153-1155.
     Google Scholar
  6. M¨ollenstedt G, Bayh W. Messung der kontinuierlichen Phasenschiebung von Elektronenwellen im kraftfeldfreien Raum durch das magnetische vektorpotential einer Luftspule. Naturwissenschaften, 1962; 49: 81-82.
     Google Scholar
  7. Boersch H, Hamisch H, Grohmann K, Wohlleben D. Experimenteller Nachweis der Phasenschiebung von Elektronenwellen durch das magnetische Vektorpotential. Z. Phys., 1961; 165: 79-93.
     Google Scholar
  8. Bocchieri P, Loinger A. Nonexistence of the Aharonov-Bohm Effect. Nuovo Cimento, 1978; 47A: 475-482.
     Google Scholar
  9. Bocchieri P, Loinger A, Siragusa G. On the Aharonov-Bohm Effect. Nuovo Cimento. 1979; 51A: 1-17.
     Google Scholar
  10. Tonomura A, Osakabe N, Matsuda T, Kawasaki T, Endo J, Yano S, Yamada H. Evidence for Aharonov-Bohm Effect with Magnetic Field Completely Shielded from Electron Wave. Phys. Rev. Lett., 1986; 56: 792-795.
     Google Scholar
  11. Osakabe N, Matsuda T, Kawasaki T, Endo J, Tonomura A, Yano S, Yamada H. Experimental Confirmation of Aharonov-Bohm Effect using a Toroidal Magnetic Field Confined by a Superconductor.Phys. Rev., 1986; A34: 815-822.
     Google Scholar
  12. Ginzburg VL, Landau LD. On the Theory of Superconductivity. Zh. Eksp. Teor. Fiz., 1950; 20: 1064-1082.
     Google Scholar
  13. Abrikosov AA, Gor’kov LP.Contribution to the Theory of Superconducting Alloys with Paramagnetic Impurities. Sov. Phys. JETP, 1961; 12: 1243-1253.
     Google Scholar