- #1
ianhoolihan
- 145
- 0
Hi all,
I'm hoping this will be a quickly solved question. In Peskin and Schroeder (2.66), when dealing with source terms in the Klein-Gordon equation, ##(\partial^2+m^2)\phi(x) = j(x)##, they have
$$\int d N =\int \frac{d^3 p}{(2\pi)^3}\frac{1}{2E_p}|\tilde{j}(p)|^2\quad \text{where}\quad\tilde{j}(p)=\int d^4y \ e^{ipy}\ j(y)$$
and ##N## is the particle number. They go on to state
1. what is meant by "resonance"
2. where being "on mass" comes into it. (I assume is to do with ##1/2E_p## being large, or some such, but I haven't figured it out.)
Cheers
I'm hoping this will be a quickly solved question. In Peskin and Schroeder (2.66), when dealing with source terms in the Klein-Gordon equation, ##(\partial^2+m^2)\phi(x) = j(x)##, they have
$$\int d N =\int \frac{d^3 p}{(2\pi)^3}\frac{1}{2E_p}|\tilde{j}(p)|^2\quad \text{where}\quad\tilde{j}(p)=\int d^4y \ e^{ipy}\ j(y)$$
and ##N## is the particle number. They go on to state
I'm a little confused by this, and was wondering if someone could explainOnly those Fourier components of ##j(x)## that are in resonance with the on-mass shell (i.e. ##p^2=m^2##) Klein-Gordon waves are effective at creating particles.
1. what is meant by "resonance"
2. where being "on mass" comes into it. (I assume is to do with ##1/2E_p## being large, or some such, but I haven't figured it out.)
Cheers