All Questions
102
questions
0
votes
1
answer
52
views
Square of the Feynman amplitude for $a +b\to c+d$ and its reverse
In quantum field theory, if a process $a +b\to c+d$ is allowed by a certain interaction Lagrangian (hermitian), the reverse process, $c+d\to a+b$, must also be allowed (as far as I understand) by the ...
- 11.8k
2
votes
0
answers
60
views
Asymptotic states and physical states in QFT scattering theory
Context
In the scattering theory of QFT, one may impose the asymptotic conditions on the field:
\begin{align}
\lim_{t\to\pm\infty} \langle \alpha | \hat{\phi}(t,\mathbf{x}) | \beta \rangle = \sqrt{Z} \...
- 108
1
vote
0
answers
101
views
Discontinuity of the scattering amplitude and optical theorem
The generalized optical theorem is given by:
\begin{equation}\label{eq:optical_theorem}
M(i\to f) - M^*(f\to i) = i \sum_X \int d\Pi_X (2\pi)^4 \delta^4(p_i-p_X)M(i\to X)M^*(f\to X).\tag{Box 24.1}
...
- 53
3
votes
0
answers
64
views
Deriving a contradiction from the LSZ condition
I'm reading the LSZ reduction formula in the wikipedia:
https://en.wikipedia.org/wiki/LSZ_reduction_formula
To make the argument simple, let $$\mathcal{L}=\frac{1}{2}(\partial \varphi)^2 - \frac{1}{2}...
- 61
3
votes
0
answers
151
views
LSZ reduction formula and connected Feynman diagrams in Peskin & Schroeder [duplicate]
I don't understand why in the LSZ reduction formula I need to consider only connected Feynman diagrams when I compute scattering amplitudes. From what I read in Peskin & Schroeder it seems that ...
- 357
2
votes
1
answer
159
views
Confusion regarding the $S$-matrix in Quantum Field Theory
In his Harvard lectures on QFT, Sidney Coleman defines the $S$-matrix as,
$$ S \equiv U_{I}(\infty, -\infty) $$
Where $U_{I}(-\infty, \infty)$ is the time evolution operator in the interaction picture....
- 322
3
votes
1
answer
183
views
Sidney Coleman's Lectures Notes on QFT: Question regarding incoming states and free states
In Sidney Coleman's Lecture Notes on Quantum Field Theory, under section 7.4, we have the following,
For a scattering of particles in a potential, we have a very simple formula for the S-matrix.
We ...
- 322
1
vote
1
answer
112
views
$S$-matrix in Dirac picture
Let's define the interaction Hamiltonian as
$$\hat{H}(t) = \hat{H}_{\text{S}}+\hat{V}_{\text{S}}(t)\tag{1}$$
Where $\hat{V}_{\text{S}}\in \mathcal{L}(\mathcal{H})$ represents time-dependent ...
user375448
2
votes
1
answer
113
views
CPT invariance and Soft Theorems
I am reading the paper IR Dynamics and Entanglement Entropy, written by Toumbas and Tomaras and I have a question on using the CPT invariance of the QED $S$-matrix elements in order to derive the ...
- 3,992
3
votes
1
answer
445
views
Asymptotic states in the Heisenberg and Schrödinger pictures
One can show that, in the interacting theory, the operators that create single-particle energy-momentum eigenstates from the vacuum are
\begin{align}
(a_p^{\pm\infty})^\dagger=\lim_{t\to\pm\infty}(...
- 1,060
2
votes
2
answers
185
views
Difference of decay amplitude and transition amplitude from initial to final state
In Zwiebachs "A First Course in String Theory" 2nd edition he states in chapter 25.2, that
"the amplitude for an initial state consisting of a $\phi$ particle to turn into a final ...
4
votes
1
answer
184
views
Why is the $S$-matrix calculated using the free vacuum state and not the full interacting vacuum state?
Let $H = H_0 + H_I$ be a Hamiltonian that is the sum of a free Hamiltonian and an interacting Hamiltonian. Denote the free vacuum state by $| 0 \rangle$ and the full vacuums state by $|\Omega \rangle$....
- 3,350
0
votes
1
answer
50
views
Why are all the possible permutationss in the perturbative $S$-matrix calculations added together?
I have a question regarding the calculation of the $S$-matrix. During the calculation of second order term of the $S$-matrix for e.g. the Møller scattering $(e^
− + e^
− → e^
− + e^
−)$ $|i\rangle=|e^...
- 172
2
votes
1
answer
106
views
Scattering Amplitude & Unitarity
In Srednicki's Quantum Field Theory chapter 11, the probability of a $2 \to n$ scattering process is calculated to be
$$
P = \frac{|\left<f|i\right>|^2}{\left<f|f\right>\left<i|i\right&...
- 148
0
votes
1
answer
87
views
Question about asymptotic assumption in LSZ reduction formula derivation
I have a silly question in derivation of LSZ reduction formular, I can go directly with the derivation until I found a assumption that I can't convince myself.
In the book Quantum Field Theory and the ...
