Maxwell Electrodynamics in Terms of Physical Potentials
A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector pote...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/7/915 |
| _version_ | 1811213374329978880 |
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| author | Parthasarathi Majumdar Anarya Ray |
| author_facet | Parthasarathi Majumdar Anarya Ray |
| author_sort | Parthasarathi Majumdar |
| collection | DOAJ |
| description | A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein’s incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator with the d’Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative Nöther coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the Aharonov−Bohm effect, where dependence of the Aharonov−Bohm phase on the physical vector potential is highlighted. |
| first_indexed | 2024-04-12T05:44:36Z |
| format | Article |
| id | doaj.art-ced4e24fa592485a9fa1ab5743addb90 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-12T05:44:36Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ced4e24fa592485a9fa1ab5743addb902022-12-22T03:45:29ZengMDPI AGSymmetry2073-89942019-07-0111791510.3390/sym11070915sym11070915Maxwell Electrodynamics in Terms of Physical PotentialsParthasarathi Majumdar0Anarya Ray1Indian Association for the Cultivation of Science, Kolkata 700032, IndiaDepartment of Physics, Presidency University, Kolkata 700032, IndiaA fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein’s incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator with the d’Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative Nöther coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the Aharonov−Bohm effect, where dependence of the Aharonov−Bohm phase on the physical vector potential is highlighted.https://www.mdpi.com/2073-8994/11/7/915n/a |
| spellingShingle | Parthasarathi Majumdar Anarya Ray Maxwell Electrodynamics in Terms of Physical Potentials Symmetry n/a |
| title | Maxwell Electrodynamics in Terms of Physical Potentials |
| title_full | Maxwell Electrodynamics in Terms of Physical Potentials |
| title_fullStr | Maxwell Electrodynamics in Terms of Physical Potentials |
| title_full_unstemmed | Maxwell Electrodynamics in Terms of Physical Potentials |
| title_short | Maxwell Electrodynamics in Terms of Physical Potentials |
| title_sort | maxwell electrodynamics in terms of physical potentials |
| topic | n/a |
| url | https://www.mdpi.com/2073-8994/11/7/915 |
| work_keys_str_mv | AT parthasarathimajumdar maxwellelectrodynamicsintermsofphysicalpotentials AT anaryaray maxwellelectrodynamicsintermsofphysicalpotentials |