0
$\begingroup$

I was trying to find the scattering amplitude using the LSZ formula for a trivial process i.e. applying it to the two-point correlation function, but I kept getting 0 as the answer.

I'm not sure exactly if this is correct or not, and, if it is, how to interpret why $\langle p_f | p_i \rangle = 0$ physically.

$\endgroup$
1

1 Answer 1

1
$\begingroup$

The $S$-matrix is often split into a trivial identity part, plus a non-trivial $T$-matrix called the "transfer matrix", for this exact reason.

$$S=1+iT$$

Furthermore, when calculating scattering amplitudes we can factor out a general momentum-conserving delta-function from $T$:

$$T=(2\pi )^4 \delta^4\left(\sum p^\mu_f - \sum p^\mu_i\right) \mathcal{M}$$

The whole framework of calculating scattering amplitudes using Feynman rules and LSZ is for calculating $i\mathcal M$. One must keep in mind how $\mathcal M$ and $S$ are related when calculating cross sections or decay rates, which directly involve $S$.

For more you may check out chapter 5 of Schwartz.

$\endgroup$
2

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.