All Questions
Tagged with quantum-field-theory s-matrix-theory
463
questions
0
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1
answer
149
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$S$-matrix from interacting picture
I’ve been reading a lot about the interaction picture, and I’m trying to string the ideas behind it together.
Essentially, the goal is to calculate something like $<f(\infty)|i(-\infty)>$. We ...
user310742
3
votes
1
answer
445
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Asymptotic states in the Heisenberg and Schrödinger pictures
One can show that, in the interacting theory, the operators that create single-particle energy-momentum eigenstates from the vacuum are
\begin{align}
(a_p^{\pm\infty})^\dagger=\lim_{t\to\pm\infty}(...
- 1,060
1
vote
0
answers
89
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LSZ Reduction Formula (Weinberg Derivation)
In section 10.3 of Weinberg's Volume 1 in deriving LSZ reduction Formula, the author says,
We also define a 'truncated' matrix element $M_l$ by
$$\int d^4 x_2 \cdots e^{-q_2x_2} <\textbf q \sigma| ...
- 96
4
votes
2
answers
215
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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
2
votes
1
answer
132
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On "waiting" and Coleman's derivation of LSZ
I'm going through the derivation LSZ in Coleman's QFT notes. The math is perfectly clear (or at least I don't mind being handwavy about convergence issues), and I'm happy with the idea that \begin{...
- 215
2
votes
2
answers
185
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Difference of decay amplitude and transition amplitude from initial to final state
In Zwiebachs "A First Course in String Theory" 2nd edition he states in chapter 25.2, that
"the amplitude for an initial state consisting of a $\phi$ particle to turn into a final ...
4
votes
1
answer
184
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Why is the $S$-matrix calculated using the free vacuum state and not the full interacting vacuum state?
Let $H = H_0 + H_I$ be a Hamiltonian that is the sum of a free Hamiltonian and an interacting Hamiltonian. Denote the free vacuum state by $| 0 \rangle$ and the full vacuums state by $|\Omega \rangle$....
- 3,350
5
votes
1
answer
575
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Vacuum, creation and annihilation operators in interacting QFT
I am reading the QFT book by M. Schwartz. More specifically, I have issues with the section about LSZ. I am puzzled with the way the creation and annihilation operators from the free theory act there.
...
- 705
0
votes
1
answer
50
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Why are all the possible permutationss in the perturbative $S$-matrix calculations added together?
I have a question regarding the calculation of the $S$-matrix. During the calculation of second order term of the $S$-matrix for e.g. the Møller scattering $(e^
− + e^
− → e^
− + e^
−)$ $|i\rangle=|e^...
- 172
2
votes
1
answer
106
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Scattering Amplitude & Unitarity
In Srednicki's Quantum Field Theory chapter 11, the probability of a $2 \to n$ scattering process is calculated to be
$$
P = \frac{|\left<f|i\right>|^2}{\left<f|f\right>\left<i|i\right&...
- 148
1
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0
answers
40
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Prefactor to amplitude for massless fermions/massive bosons
I was reviewing some of my old notes and found this formula for a matrix elements between two states:
$$
<f|S|i>= \delta_{fi} + [(2\pi)^4 \delta^4(P_f - P_i) \prod_{ext. fermion}\left(\frac{m}{...
1
vote
0
answers
75
views
How do we measure the gluon scattering?
In QFT, we often calculate the 'Feynman amplitude' for gluon scattering. As we know, Gluon is gauge boson mediating the strong force between quarks. By color confinement, Quarks are never seen in our ...
- 108
1
vote
1
answer
120
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Understanding from $S$-Matrix to Feynman-Rules in scalar QFT [closed]
I am learning QFT at the moment and the process from defining the S-Matrix to deriving the feynman rules is in my opinion pretty complicated, since there are many different things to pay attention to. ...
- 505
0
votes
0
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61
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Calculating Diagrams with Wilson Lines to One Loop
I have a question concerning the calculation of amplitudes containing Wilson lines.
I want to calculate the jet function defined by equation (3.3) from this paper.
$$\mathcal{J}(\text{arguments})u_s(p)...
- 2,983
4
votes
2
answers
161
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Are amplitudes for inverse processes related to each other?
The (generalized) optical theorem is presented in the book of Peskin and Schroeder (An introduction to Quantum Field Theory - chapter 7-Radiative Corrections:Some Formal Developments) as follows
$-i (\...
