Polarization-Magnetization Tensor

[Vectronix]

Please forgive me if I chose the wrong thread level. I don't think this is an undergrad topic but I'm not sure. I'm looking for some info about the polarization-magnetization tensor; I can't seem to find it anywhere.

 

[DrDu]

The polarisation magnetisation tensor $P_{\mu \nu}$ may be seen to be a consequence of the conservation of the charges inside a material. If $j_\rho$ is the charge current density vector, then charge conservation means $\partial^\mu j_\mu=0$. This will be fulfilled for any j fulfilling $j_\mu=\partial^\nu P_{\nu\mu}$ where $P_{\mu\nu}=-P_{\nu\mu}$. However, this does not specify the tensor $P$ completely, as P is defined only up to a solution of the homogeneous equation $\partial^\nu P^\text{hom}_{\nu\mu}=0$. In optics this freedom is used to set the magnetisation to zero.

 

[Dale]

A little about the magnetization polarization tensor is given here:

https://en.m.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism

 

[Vectronix]

Thank you for the information. I have a question though: why are electric polarization and magnetization considered to be one entity like space and time, like energy and momentum?

 

[Dale]

Thank you for the information. I have a question though: why are electric polarization and magnetization considered to be one entity like space and time, like energy and momentum?

Because magnetization in one frame is magnetization and polarization in another frame.