Unformatted text preview: reference frame. 2b) What equation does Ψ have to satisfy in order that you can work with an A μ that satisﬁes, ∇ · A = 0 or ∇ · A + ∂ Φ /∂t = 0, even if A μ doesn’t have these properties? 3) Show explicitely that Eqs. 5.46 and 5.47 in your notes yield Maxwell’s 4 equations. 4) You are familiar with the completely antisymmetric tensor in 3D, ± ijk . In 4D one can similarly deﬁne a completely antisymmetric tensor ± ijkn , with ± 0123 ≡ 1 and interchange of any two indices means multiplication by 1. And of course if any two indices are the same the tensor is zero. Evaluate ± μναβ F μν F αβ and note that it is a Lorentz invariant. Can you think of an easy explanation why without doing any explicit calculations. 1...
View
Full Document
 Spring '10
 Blecher
 Current, Magnetism, Angular Momentum, Friction, Inertia, Special Relativity, outer radius ro, radius Ri, inner radius ri, completely antisymmetric tensor

Click to edit the document details