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...
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 Spring '10
 Blecher
 Current, Magnetism, Angular Momentum, Friction, Inertia, Special Relativity, outer radius ro, radius Ri, inner radius ri, completely antisymmetric tensor

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