(a) Construct a tensor D v (analogous to F v ), out of D and H Use it to express Maxwell 's equations inside matter in terms of the free current density J f (b) Construct the dual tensor H v (analogous to G v (c) Minkowski proposed the relativistic constitutive relations for linear media where is t...

a D E P suggests ED HBM suggests B H EDcD B H Then b Then following the derivation on p 539 Huv 0 bu ...

(a) Construct a tensor D v (analogous to F v ), out of D and H. Use...

Question:

(a) Construct a tensor D^μv (analogous to F^μv), out of D and H. Use it to express Maxwell's equations inside matter in terms of the free current density J^μ_f.

(b) Construct the dual tensor H^μv (analogous to G^μv.

(c) Minkowski proposed the relativistic constitutive relations for linear media: where ε is the proper²⁰ permittivity, μ is the proper permeability, and η^μ is the 4-velocity of the material. Show that Minkowski's formulas reproduce Eqs. 4.32 and 6.31, when the material is at rest.

(d) Work out the formulas relating D and H to E and B for a medium moving with (ordinary) velocity u.