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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^{μ}δ_{μ}η^{ρ}- η^{μ}δ_{μ}ε^{ρ}= ζ^{η}

and the monster one :

[p_{ε},p_{η}] = [p_{μ}ε^{μ},p_{β}η^{β}] = (p_{μ}ε^{μ})∂_{μ}(p_{β}η^{β}) -

(p_{μ}η^{μ})∂_{μ}(p_{β}ε^{β})

Thanks,

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# MTW Exercise 25.5 b) - killing vectors

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