All Questions
16
questions
0
votes
0
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60
views
How can I calculate the cross-section of a $N+\pi \rightarrow N + \pi$?
In the same theme as my previous question, I have the diffusion process $$N+\pi \rightarrow N + \pi$$ where the Lagrangian for this theory is
$$L = \partial^\mu\psi\partial_\mu\psi^* - M²\psi\psi^*-\...
- 11
1
vote
1
answer
112
views
How do we interpret disconnected diagrams in scattering theory?
It is apparent that disconnected diagram contributes additional delta functions to the corresponding matrix element. For example, we consider the scalar $\phi^3$ theory and the following $2\...
- 619
4
votes
2
answers
215
views
What are wave packets for (probabilities from the $S$-matrix)?
I am looking into the section of the book by Peskin and Schroeder in which they connect the $S$-matrix to probabilities.
They start by considering the in state, which is a two-particle state
\begin{...
- 705
4
votes
2
answers
416
views
Optical theorem Peskin and Schroeder
I'm trying to understand the optical theorem of Peskin and Schroeder
$$\tag{7.50} \text{Im} M(k_1,k_2\rightarrow k_1,k_2)=2E_{cm}p_{cm}\sigma_{tot}(k_1,k_2\rightarrow\text{anything})$$
which Peskin ...
- 789
4
votes
1
answer
207
views
QFT- Computing matrix elements when momentum is NOT conserved
In QFT, when computing cross sections one calculates the $T$ matrix elements (probability amplitudes that the interaction Hamiltonian takes us from the initial state $|\mathbf{k}_A,\mathbf{k}_B\big>...
- 93
3
votes
0
answers
249
views
How to study the calculation of scattering amplitudes in particle physics?
I am looking for literature on the topic of calculating scattering amplitudes for particle physics processes, but this is a very big subject.
I have studied introductory particle physics before, as ...
1
vote
1
answer
158
views
QFT scattering with classical potential
I'm studying chapter 6 section 2 of Peskin and Schroeder, on page 185 the unnumbered equation between 6.29 and 6.30, we are trying to compute the $S$-matrix element of the scattering of an eletron ...
- 789
5
votes
0
answers
98
views
Form of the optical theorem in non-Abelian theory
I am studying chapter 16.3 from Peskin & Schroeder and I am trying to follow through the argument where we include contributions from ghosts to satisfy the Ward identity in non-Abelian gauge ...
- 2,035
5
votes
1
answer
801
views
Trouble deriving expression for differential scattering cross section from $S$-matrix
I am following the derivation of the scattering cross-section from Peskin and Schroeder textbook. On page 105, we get an expression for the differential cross-section:
$$d\sigma = \left(\prod_f \frac{...
- 316
1
vote
1
answer
734
views
Unitarity and amplitudes
In Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory there are few statements about analytical structure of amplitudes.
I want to understand statement:
In a local theory of ...
- 5,707
6
votes
2
answers
450
views
Why amplitudes are rational functions?
In Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory there are few statements about analytical structure of amplitudes.
I want to understand statement:
Tree amplitudes must ...
- 5,707
2
votes
1
answer
257
views
Crossing Symmetry between tree-level diagrams of $e^+ e^- \rightarrow \mu^+ \mu^-$ and $e^- \mu^- \rightarrow e^- \mu^-$
According to Peskin and Schroeder (P&S)'s book, on pp. 156-157, the two processes $e^+ e^- \rightarrow \mu^+ \mu^-$ and $e^- \mu^- \rightarrow e^- \mu^-$ are connected via $s \leftrightarrow t$ ...
- 353
1
vote
1
answer
2k
views
Mass dimension of an $n$-particle scattering amplitude in 4D
For the 4-dimensional case, and using the cross-section formula, how can we show that the mass dimensions of an $n$-particle amplitude must be $$[A_n] = 4-n~?\tag{2.99}$$
My understanding is that the ...
- 65
3
votes
1
answer
253
views
Why do particle resonances lead to peaks in the cross section?
Since bound states lead to poles in Green functions, I wonder if this is the reason for peaks in the cross section.
From a QFT point of view, the infinitesimal cross section $\text d\sigma/\text d\...
- 2,648
6
votes
1
answer
261
views
S-Matrix Interpretation and Predictions
How does one distinguish between the second-loop contribution of a known particle, and the first-loop contribution of a more massive-and as yet undiscovered-particle in the S-matrix and/or ...
- 321