Electromagnetic fields with symmetry

Authors

DOI:

https://doi.org/10.31349/RevMexFisE.21.020201

Keywords:

Electromagnetic fields, symmetries, constants of motion, Lorentz transformations

Abstract

We show that if an electromagnetic field is invariant under translations or rotations, three of the six components of the field can be expressed in terms of a (gauge-invariant) scalar potential which is also invariant under these transformations. This scalar potential appears in the constant of motion associated with this symmetry for a charged test particle in this field. We also show that the Cartesian components of the electromagnetic field can be combined to form two SO(2, 1) vectors

References

G. F. Torres del Castillo and A. Moreno Ruiz, Symmetries of the equations of motion that are not shared by the Lagrangian, arXiv:1705.08446 (2017)

G. F. Torres del Castillo, An Introduction to Hamiltonian Mechanics, (Springer, Cham, 2018). Sec. 2.5. https://doi.org/10.1007/978-3-319-95225-3

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998)

G. F. Torres del Castillo, The linear and the angular momentum stored in a distribution of charges in a magnetic field, Rev. Mex. Fıs. 69 (2023) 050701. https://doi.org/10.31349/RevMexFis.69.050701

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Published

2024-07-01

How to Cite

[1]
G. F. Torres del Castillo, “Electromagnetic fields with symmetry”, Rev. Mex. Fis. E, vol. 21, no. 2 Jul-Dec, pp. 020201 1–, Jul. 2024.

Issue

Vol. 21 No. 2 Jul-Dec (2024): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2024 Gerardo Francisco Torres del Castillo

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Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.