All Questions
97
questions
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
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 $$\mathcal{L}=\frac{1}{2}(\partial \varphi)^2 - \frac{1}{2}...
- 61
2
votes
0
answers
77
views
LSZ theorem for trivial scattering
The $1\to1$ scattering amplitude is trivial and is given by (take massless scalars for simplicity)
$$
\tag{1}
\langle O(\vec{p}) O^\dagger(\vec{p}\,')\rangle = (2 | \vec{p}\,|) (2\pi)^{D-1} \delta^{(...
- 181
-3
votes
1
answer
91
views
Some calculation in Mahan book, p73 [closed]
On page 73 of Mahan, Many-particle physics, 3rd edition, one finds
$$
_0\langle|S(-\infty,0) = e^{-iL}_0\langle|S(\infty,-\infty)S(-\infty,0).
$$
I'm wondering why this is true, as in the previous ...
- 793
17
votes
2
answers
1k
views
What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?
For background, I'm primarily a mathematics student, studying geometric Langlands and related areas. I've recently been trying to catch up on the vast amount of physics knowledge I'm lacking, but I've ...
- 171
3
votes
2
answers
363
views
Proof that asymptotic particle states are free
In quantum field theory, It’s often said that the interacting annihilation operator (defined by the Klein Gordon inner product between the interacting field and a plane wave) behaves like the free ...
user310742
2
votes
0
answers
60
views
How to perform the limit of infinite time in the LSZ approach?
I am computing the scattering matrix using the LSZ reduction formula in a semiclassical limit. The result that I am getting has the following form:
$$
S = \lim_{t_i \to - \infty} \lim_{t_f \to \infty} ...
- 81
3
votes
1
answer
445
views
Asymptotic states in the Heisenberg and Schrödinger pictures
One can show that, in the interacting theory, the operators that create single-particle energy-momentum eigenstates from the vacuum are
\begin{align}
(a_p^{\pm\infty})^\dagger=\lim_{t\to\pm\infty}(...
- 1,060
1
vote
0
answers
89
views
LSZ Reduction Formula (Weinberg Derivation)
In section 10.3 of Weinberg's Volume 1 in deriving LSZ reduction Formula, the author says,
We also define a 'truncated' matrix element $M_l$ by
$$\int d^4 x_2 \cdots e^{-q_2x_2} <\textbf q \sigma| ...
- 96
4
votes
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
5
votes
1
answer
576
views
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
1
vote
0
answers
40
views
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
1
answer
120
views
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
4
votes
2
answers
161
views
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 (\...
1
vote
0
answers
136
views
Work of LSZ reduction formula
I want to know the mechanism of the LSZ reduction formula. The left side will have $\langle f|S|i\rangle$ and the right side has Fourier transform of $(\Box+m^2)$ times multiplication of Heisenberg ...
- 534