Electromagnetic fields with symmetry





Electromagnetic fields, symmetries, constants of motion, Lorentz transformations


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


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




How to Cite

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