Linked Questions
16 questions linked to/from Scattering, Perturbation and asymptotic states in LSZ reduction formula
2
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LSZ reduction derivation Srednicki [duplicate]
In the derivation of the LSZ reduction formula equation (5.21) Srednicki claims that in case of an interaction term in the Lagrangian density $a^{\dagger}(\textbf{k})$ will no longer be time dependent....
- 353
14
votes
2
answers
2k
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On the interpretation of Feynman diagrams
I am currently trying to find out about what exactly Feynman diagrams are, and up until now I have mainly used the lecture notes 'Mathematical ideas and notions of quantum field theory' by Etingof. In ...
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5
votes
2
answers
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The use of $a^\dagger(\mathbf{k}) = -i \int d^3x e^{ikx}\stackrel{\leftrightarrow}{\partial}_0 \phi(x)$ in the derivation of the LSZ-formula
I noticed that in Srednicki's derivation of the LSZ-formula the expression (chapter 5) for the creation (and also later for the annihilation) operator by the field operator:
$$a^\dagger(\mathbf{k}) = -...
- 10.2k
4
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3
answers
1k
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The contradiction between Gell-mann Low theorem and the identity of Møller operator $H\Omega_{+}=\Omega_{+}H_0$
This question originates from reading the proof of Gell-mann Low thoerem.
$H=H_0+H_I$, let $|\psi_0\rangle$ be an eigenstate of $H_0$ with eigenvalue $E_0$, and consider the state vector defined as
$$|...
- 6,081
7
votes
2
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879
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QFT - Why do in and out states have a non-trivial overlap?
I'm trying to follow chapter 4 about interacting fields in Peskin and Schröder. They define the S-matrix by
$$_{\mathrm{out}}\langle p_1 p_2 | k_a k_b\rangle_{\mathrm {in}} = \langle p_1 p_2 | S | k_a ...
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11
votes
2
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826
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How to replace $T$-product with retarded commutator in LSZ formula?
I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246:
Here, they consider the elastic scattering of particle $A$ off particle $B$:
...
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3
votes
1
answer
730
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Confusion about modes and quantum field theory
I'm learning quantum field theory from P&S and Srednicki. I'm having a lot of difficulties understanding the concept of a momentum state. In particular, I'm confused about how to interpret the ...
user299467
3
votes
3
answers
353
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Are the photons that we detect with our eyes virtual? [duplicate]
From asking several questions about virtual particles on this website, the most popular consensus (on PSE at least) seems to be that they are nothing more than a convenient way of expressing a ...
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3
votes
2
answers
414
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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
5
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1
answer
773
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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.
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6
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1
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What is the role of wave packets in LSZ formulae?
When deriving LSZ formulae, we assume asymptotic particles’ creation/annihilation operators as:
$$a_\text{g,in/out}\ \ (\mathbf{p})\equiv \int d^3k \ g(\mathbf{k}) a_\text{in/out}(\mathbf{k}), \ \text{...
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1
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1
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I really wonder about the time derivative of creation and annihilation operators in the derivation of LSZ
On p. 71 below eq. (6.12) in Schwartz book, they assume that
$$\lim_{t \to \pm\infty}\partial_0 a_p(t)=0.\tag{1}$$
But I thought that this is just an assumption. So we have to construct the ...
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3
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1
answer
472
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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}(...
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4
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0
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265
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Why does $U(+\infty,-\infty)|0\rangle= e^{i \theta}|0\rangle$ hold ? i.e. time evolution of vacuum is still a vacuum
In quantum field theory, we always use $U(+\infty,-\infty)|0\rangle= e^{i \theta}|0\rangle$, where $$U(+\infty,-\infty)=\lim_{\epsilon\rightarrow +0} \mathcal{T}\exp\{i \int_{-\infty}^{+\infty} e^{-\...
user153663
3
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0
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177
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How can LSZ formalism deal with "glancing blows"?
My recent answer to the question Scattering, Perturbation and asymptotic states in LSZ reduction formula got me thinking again about wave packets and the LSZ reduction formula.
In my answer, I claim ...
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