User:Maschen/Relativistic electromagnetic dipole moments

In special relativity, the electric dipole moment d and magnetic dipole moment μ of a particle transform together under Lorentz transformations.

Dipole moment tensor[edit]

The electric dipole moment d and magnetic dipole moment μ of a particle are unified into a single tensor^[1]

\sigma ^{\mu \nu }={\begin{pmatrix}0&d_{x}&d_{y}&d_{z}\\-d_{x}&0&\mu _{z}/c&-\mu _{y}/c\\-d_{y}&-\mu _{z}/c&0&\mu _{x}/c\\-d_{z}&\mu _{y}/c&-\mu _{x}/c&0\end{pmatrix}},

[www.jpier.org/PIERB/pierb47/13.12110903.pdf]

[www.physics.princeton.edu/~mcdonald/examples/movingdipole.pdf]

^ Barut, A.O. Electrodynamics and the Classical theory of particles and fields. Dover. p. 73. ISBN 978-0-486-64038-9. No factor of c appears in the tensor in this book because different conventions for the EM field tensor.