- #1
Alex Cros
- 28
- 1
Im following Weinberg's QFT volume I and I am tying to show that the following equation vanishes at large spatial distance of the possible particle clusters (pg 181 eq 4.3.8):
[tex] S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' . x_1'}... [/tex]
(i.e the Fourier of the connected part of the corresponding S matrix element) vanishes when the distance between any two particles (states) is great.
He says that this only happens when this matrix element contains precisely one single delta function that ensures 3-momentum conservation:
[tex] S_{p_1'p_2'... , p_1 p_2}^C = \delta^3(p_1'+p_2'+... - p_1 - p_2)\times \delta(energy \ conservation) \times C_{p_1'p_2'... , p_1 p_2} [/tex]
Can somebody tell my how this makes the first equation vanish when the relative distance of some states is large?
PD: sorry for the poor explanation but I am not going to explain it better than Weinberg, I am just pointing out where I am having troubles.
[tex] S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' . x_1'}... [/tex]
(i.e the Fourier of the connected part of the corresponding S matrix element) vanishes when the distance between any two particles (states) is great.
He says that this only happens when this matrix element contains precisely one single delta function that ensures 3-momentum conservation:
[tex] S_{p_1'p_2'... , p_1 p_2}^C = \delta^3(p_1'+p_2'+... - p_1 - p_2)\times \delta(energy \ conservation) \times C_{p_1'p_2'... , p_1 p_2} [/tex]
Can somebody tell my how this makes the first equation vanish when the relative distance of some states is large?
PD: sorry for the poor explanation but I am not going to explain it better than Weinberg, I am just pointing out where I am having troubles.