Covariant Maxwell Equations in Materials

[EsPg]

Hi everybody,

I have this simple question. ¿Where can I find the covariant maxwell equations in materials?. I've already one and proved they correctly represent the non-homogene maxwell equations, is this one

$$\partial_{\nu}F^{\nu\mu}+\Pi^{\mu\nu}A_{\nu}=J^{\mu}_{libre}$$

with the tensor defined as

$$\Pi_{\mu\nu}&=\chi_e(\eta_{\mu\nu}\partial^2 -\partial^{\mu}\partial^{\mu})-\de{\chi_e+\frac{\chi_m}{1+\chi_m}}\eta_{\mu l}\eta_{\nu m}(\delta_{lm}\bigtriangledown^2-\partial_{l}\partial_{m})$$

I need the other one. Thanks!

 

[EsPg]

¿Nobody? I've been checking Landau's book but i can't find them :'(. There's a Wikipedia article but it's all messed,maybe after this and on vacation I fix it.

 

[PhilDSP]

They're described and analyzed here: "Foundations of Electrodynamics" by P. Moon and D. E. Spencer.

But the whole situation becomes extremely messy as most every physical parameter including permittivity and permeability becomes skewed due to the attempt to accommodate the Lorentz Transformation.

 

[EsPg]

They're described and analyzed here: "Foundations of Electrodynamics" by P. Moon and D. E. Spencer.

But the whole situation becomes extremely messy as most every physical parameter including permittivity and permeability becomes skewed due to the attempt to accommodate the Lorentz Transformation.

Thanks. The problem is that i haven't been able to check that book, it's neither in the library nor online. ¿Any other place?

 

[Andy Resnick]

You may be able to get some insight from Post's "Formal Structure of Electromagnetics".

 

[DrDu]

I think the other one is identically equal to the equation in vacuo.
However, your equation does seem to be rather specialized. E.g. , a splitting into chi_e and chi_m seems only to be true in linear electrodynamics of non-chiral materials. Furthermore, it neglects spatial dispersion. All is discussed very well in the book of Landau.