Hi,In Mandl&Shaw, when we calculate the covaiant commutation

  • Thread starter lornstone
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  • #1
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Hi,

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!
 

Answers and Replies

  • #2


You can't Lorentz transform a time-like interval into a space-like interval. The Minkowski norm
[tex]
t^2 - x^2 - y^2 - z^2
[/tex]
is invariant under Lorentz transformations, so a time-like interval (positive norm) cannot be mapped into a space-like interval (negative norm).
 
  • #3
6
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I got it, thank you!
 

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