Landau & Lifshitz "Classical theory of fields" section 6 p. 19 define: $$ df^{ik} = dx^i dx'^k - dx^k dx'^i $$ and $$ df^{*ik}=\frac{1}{2} \; \epsilon^{iklm}df_{lm} \tag{6.11} $$ and states: "It is obvious that $df^{ik} df^*_{ik}=0$." I am unable to see that this is true. Can anyone help me?

I've just started looking at plasmas and I have some confusion. A metal is a lattice of positive ions bathed in a sea of delocalised electrons and conducts electricity. A plasma is a 'gas' of free ions and electrons and can also conduct electricity. Is a metal a solid-state plasma? Are all ionize...

I understand that there are three velocities in play in a circuit (I haven't studied Physics past high school so give me some rope) v1: the velocity by which the electrical field propagates through the conductor (equal to the speed of light) v2: the velocity of the free electrons in the wire. F...

I understand that, at the more fundamental physical level, waves are phenomena of Fields. Like electromagnetic waves of the electromagnetic field. However, I also know that we can have waves in Mediums. Like water waves in ocean water. So, are those mediums, a kind of field? Is the ocean a field?...