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Dirac delta 4D

  1. May 20, 2013 #1
    in a 4D space time, ¿what is de descomposition of de distribution:

    [tex] \delta^{(4)} (P_x+P_y-P_z-P_t)[/tex] ???

    i think that is equal to

    [tex] \delta^{(4)} (P_x+P_y-P_z-P_t)=\delta(P_x) \delta(P_y)\delta(-P_z)\delta(-P_t)[/tex],
    but, i dont understand.....
  2. jcsd
  3. May 20, 2013 #2


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    Well it's not that, but it's not clear that your expression makes sense in the first place. ##P_x+P_y-P_z-P_t## is a number, though not a Lorentz scalar. However, the object that we'd call

    $$ \delta^{(4)}(a^\mu) = \delta(a^0) \delta(a^1) \delta(a^2) \delta(a^3)$$

    takes a 4-vector as it's argument. Something like ##\delta^{(4)}(P^\mu)## would make sense, but ##\delta^{(4)}(P^t)## does not.

    Perhaps you could explain where you found that expression.
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