(a) Construct a tensor Dμν (analogous to Fμν) out of D and H. Use it to express Maxwell’...

(a) Construct a tensor D^μν (analogous to F^μν) 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^μν (analogous to G^μν).

(c) Minkowski proposed the relativistic constitutive relations for linear media:

Where is the proper³⁰ 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.

Reference equation 4.32

Reference equation 6.31

B = μH,