Abstract
The conceptual emergence of the magnetic vector potential is explored historically and mathematically in both classical and quantum physics. It was first defined by Michael Faraday as the electrotonic state and then formulated as a vector potential for the magnetic field by James Clerk Maxwell. We argue that magnetic field lines highlight axes of rotation of electromagnetic momentum and demonstrate that the magnetic vector potential takes the form of a ring vortex around a current element. In light of the Aharanov-Bohm effect, the physical existence of the magnetic vector potential field is defended. Finally we touch on the Aharanov-Casher effect and geometric phases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Aharonov and Bohm [23] also proposed an similar experimental setup showing the interference effect of the electric scalar potential in a region with an electric field free region. The relative phase change is then given by a time integral of the potential differences.
References
American Physical Society, APS News 17(7) (2008). https://www.aps.org/publications/apsnews/200807/physicshistory.cfm
A.K.T. Assis, J.P.M.C. Chaib, Ampère’s Electrodynamics (Montreal, Apeiron, 2015)
C.S. Potts, H.C.P. Richards, H. Khunrath, Electricity: Its Medical and Surgical Applications, Including Radiotherapy and Phototherapy (Lea & Febiger, Philadelphia, New York, 1911)
J.M. Thomas, Michael faraday and The Royal Institution: The Genius of Man and Place (Taylor & Francis, Oxford, 1991)
M. Faraday, The Correspondence of Michael Faraday, vol. 1 (London, The Institution of Engineering and Technology, 1991), pp. 1811–1831
W.H. Oskay, Creative Commons: Attribution 2.0 Generic—creativecommons.org/licenses/by/2.0/. www.evilmadscientist.com (2010)
A.W. Poyser, Magnetism and Electricity: A Manual for Students in Advanced Classes (Longmans, Green, & Co., New York, 1892)
M. Geupel, Deviant Art (2011). https://racoonart.deviantart.com/art/humming-top-198925449
M. Faraday, Experimental Researches in Electricity, vols. 1 and 2 (Taylor and Francis, London, 1839)
S.P. Israelsen, The Purdue Historian 7(1), 1–16 (2014)
J. Bence, The Life and Letters of Faraday (Longmans, Green and Co, London, 1870)
J.C. Maxwell, A Treatise on Electricity and Magnetism (Clarendon Press, Oxford, 1873)
J.C. Maxwell, Philos. Mag. Ser. 23(151), 12–24 (1861)
A. Einstein, Die Naturwissenschaften 14(11), 223–224 (1926)
C.N. Yang, Phys. Today 67(11), 45–51 (2014)
H. Lamb, Hydrodynamics (C.J. Clay and Sons, London, 1895)
P. Tait, Lectures on Some Recent Advances in Physical Science (MacMillan & Co., London, 1876)
A.C.T. Wu, C.N. Yang, Int. J. Mod. Phys. A 21(16), 3235–3277 (2006)
M.J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (University of Notre Dame Press, London, 1967)
R.P. Feynman, R.B. Leighton, M.L. Sands, The Feynman Lectures on Physics, Vol. I and II (Addison-Wesley, 1963)
D.J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, New Jersey, 1995)
J.D. Jackson, L. Okun, Rev. Mod. Phys. 73(3), 663–680 (2001)
Y. Aharonov, D. Bohm, Phys. Rev. 115(3), 485–491 (1959)
R.G. Chambers, Phys. Rev. Lett. 5(1), 3–5 (1960)
Tonomura, Phys. Rev. Lett. 56(8), 792–795 (1986)
Y. Aharonov, D. Bohm, Phys. Rev. 123(4), 1511–1524 (1961)
M.V. Berry, R.G. Chambers, M.D. Large, C. Upstill, J.C. Walmsley, Eur. J. Phys. 1(3), 154–162 (1980)
Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319–321 (1984). https://doi.org/10.1103/PhysRevLett.53.319
M.V. Berry, Proc. R. Soc. London. Ser. A. Math. Phys. Sci. 392(1802), 45–57 (1984). https://doi.org/10.1098/rspa.1984.0023
S. Chaudhary, M. Endres, G. Refael, Phys. Rev. B 98, 064310 (2018). https://doi.org/10.1103/PhysRevB.98.064310
E. Cohen, H. Larocque, F. Bouchard, F. Nejadsattari, Y. Gefen, E. Karimi, Nat. Rev. Phys. 1(7), 437–449 (2019). https://doi.org/10.1038/s42254-019-0071-1
B. Simon, Phys. Rev. Lett. 51, 2167–2170 (1983). https://doi.org/10.1103/PhysRevLett.51.2167
C.N. Yang, Tsinghua Sci. Technol. 3(1), 861–970 (1998)
M. Nakahara, Geometry, Topology and Physics (Taylor & Francis Group, 2003)
R. Healey, Gauging What’s Real: The Conceptual Foundations of Gauge Theories (Oxford University Press, 2007)
E. Noether, Transp. Theory Stat. Phys. 1(3), 186–207 (1971)
K.A. Brading, Stud. History Philos. Mod. Phys. 33, 3–22 (2002)
A. Lasenby, C. Doran, S. Gull, Philos. Trans. R. Soc. Lond. 356(1737), 487–582 (2004)
D.J. Griffiths, Introduction to Elementary Particles (John Wiley & Sons, New York, 1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Klausen, K.Ó. (2020). Conceptual Emergence. In: A Treatise on the Magnetic Vector Potential. Springer, Cham. https://doi.org/10.1007/978-3-030-52222-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-52222-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-52221-6
Online ISBN: 978-3-030-52222-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)