MTW Exercise 25.5 b) - killing vectors

hi there,

In this Ex ( see attached snapshot ), point b), the poisson bracket equation is not so straightforward to obtain.

Please correct my Poisson Bracket expansion here :

The first one which is provided is simpler :

[ε,η] = ε^μδ_μη^ρ - η^μδ_με^ρ = ζ^η



and the monster one :



[p_ε,p_η] = [p_με^μ,p_βη^β] = (p_με^μ)∂_μ(p_βη^β) -

(p_μη^μ)∂_μ(p_βε^β)



Thanks,

Attached Images

MTWExc25_5.png (68.3 KB)

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