All Questions
24
questions
2
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0
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60
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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
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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
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
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
2
votes
0
answers
193
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Vacuum loop in $\phi^4$ scattering
$\newcommand{\Ket}[1]{\left|#1\right>}$
$\newcommand{\Bra}[1]{\left<#1 \right| }$
I am studying QFT through Peskin & Schroeder's book and currently I am doing the part of scattering in $\phi^...
- 21
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 ...
1
vote
1
answer
166
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On the asymptotic condition
The text that I am following is John Taylor's Scattering Theory. This relates specifically to page 28 and 29 where we discuss the asymptotic condition in quantum mechanics. What I am ultimately ...
- 6,963
3
votes
0
answers
176
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Why do we get away with these assumptions of scattering theory?
The first questionable assumption I can think of is: The integration of the Hamiltonian density in the Dyson series is done over an infinite spacetime volume.
Why do we get away with this assumption? ...
- 6,355
2
votes
0
answers
148
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Wave function of a real scalar field in interacting quantum field theory
In interacting real scalar field theory, if I intuitively define the "wave function" of a state as
$$\Psi(x)\equiv\langle\Omega|\hat{\phi}(x)|\Psi\rangle.$$
Does this wave function satisfy ...
- 21
7
votes
1
answer
747
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Confusion about in and out states, interacting Hilbert space etc, referring to Weinberg QFT
There are many posts related to this issue on this site, but I have found none that answer my specific questions about this matter.
I review my understanding of Weinbergs approach. There are probably ...
- 1,129
2
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0
answers
178
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Interaction vacuum and free vacuum states [closed]
Why we prepare in and out states from interacting vacuum rather than free vacuum even if the total Hamiltonian is just free Hamiltonian at times far past and far future? What is really the difference ...
- 21
3
votes
1
answer
136
views
Is the $S$-matrix a scalar operator?
The scattering $S$ operator which is defined to be the operator corresponding to $S$ matrix should be rotational invariance, does this imply $S$ operator is a scalar operator?
- 377
1
vote
1
answer
339
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In/out states in scattering theory, Weinberg vol 1
Chapter 3 of volume 1 of Weinberg's QFT says the following regarding in and out states in scattering theory:
Implicit in the definition of the states is a choice of the inertial frame from which the ...
- 1,593
1
vote
0
answers
77
views
Dependence of $S$-matrix on a coordinate system in QFT
The $S$-matrix is defined as follows (see e.g. Section 3.2 in Weinberg's "The quantum theory of fields"):
$$S=\lim\exp(iH_0\tau)\exp(-iH(\tau-\tau_0))\exp(-iH_0\tau_0),$$
where the limit is taken when ...
- 2,226
4
votes
2
answers
247
views
Contradiction between aymptotically free particles in QFT and unlocalization
When studying different interactions in any QFT, one always assumes that the IN and OUT states are asymptotically free particles with definite momenta. For example, one assumes that an electron and a ...
- 63