The Fourier-Minkowski transform?

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Can anyone suggest any references explaining the motive behind it's definition?

I'm unfortunately too thick to see the necessity of the sign of the time part of the exponentials being opposite to that of the space part. It seems that the transform must preserve some property of the invariance of the space time interval, but i don't see what.

Thanks
 
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Isn't it just a convention to ensure that the 4-momentum operator can be represented as i\partial_\mu (when we Fourier transform a wave function)?

This question has been asked a couple of times recently, but I don't think I read the answers. Try searching for it.
 

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