Monday, 23 April 2018

Exercise 1.11 Maxwell in Relativity

The question was

Verify that (1.98) is indeed equivalent to (1.97), and that they are both equivalent to the last two equations in (1.93).

My answer was

We had

The last two of these are Maxwell's electromagnetic field equations written as tensors.

We also had the electromagnetic field strength tensor, which was claimed to be


The first part of the question is easy: Expand ∂Fνλ] according to the recipe in (1.80).

The second part is more intimidating because, equation (1.98) looks like a monster. It is really 64 equations for all possible values of μ,ν,λ. However, when you work them out, due to the much redundancy and the antisymmetry of Fμν we are left with only four! 

For details of my answer click here.

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