Analysis of 4D Space-Time Distribution

[alejandrito29]

in a 4D space time, ¿what is de descomposition of de distribution:

$$\delta^{(4)} (P_x+P_y-P_z-P_t)$$ ?

i think that is equal to

$$\delta^{(4)} (P_x+P_y-P_z-P_t)=\delta(P_x) \delta(P_y)\delta(-P_z)\delta(-P_t)$$,
but, i don't understand...

 

[fzero]

in a 4D space time, ¿what is de descomposition of de distribution:

$$\delta^{(4)} (P_x+P_y-P_z-P_t)$$ ?

i think that is equal to

$$\delta^{(4)} (P_x+P_y-P_z-P_t)=\delta(P_x) \delta(P_y)\delta(-P_z)\delta(-P_t)$$,
but, i don't understand...

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.