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In Mandl&Shaw, when we calculate the covaiant commutation relations for a scalar field we obtain :

[tex] [\phi(x),\phi(y)]= i\Delta(x-y)=0[/tex]

and the last equality stands if x-y is a space-like interval. But I don't understand why. We know that it is zero if the time component is zero and we also know that delta is invariant under proper Lorentz transformation. I don't see why we can't do the correct lorentz transformation (which bring time to zero) with a time-like interval so that it is also zero.

Thank you!