All Questions
Tagged with quantum-field-theory s-matrix-theory
463
questions
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 $$\mathcal{L}=\frac{1}{2}(\partial \varphi)^2 - \frac{1}{2}...
- 61
1
vote
1
answer
74
views
Quantization of a massless scalar
Let $t$:time, $r$:distance, and $u=t-r$.
Since any massless particle should propagate along u=const. , we need to change the asymptotic infinity of a massless scalar from time infinity to null ...
- 11
2
votes
1
answer
114
views
Schrodinger's picture and Heisenberg's picture in finding interaction ground state and two-point correlator
In section 4.2 of An Introduction to Quantum Field Theory by M.E.Peskin and others, it derives interaction ground state by observing the time evolution of ground state in free field theory (pg.86), ...
- 529
3
votes
1
answer
121
views
Explict Form of Ground State in Interacting Field Theory
In An Introduction to Quantum Field Theory by Peskin and Schroeder chapter 4, it has discussed about the ground state $|\Omega\rangle$ (where $|0\rangle$ is the ground state in free field theory) in ...
- 529
4
votes
2
answers
296
views
Derivation of Peskin & Schroeder eq. (4.29)
Background material:
These are the parts that I can follow.
Previously Peskin & Schroeder have derived already the expression of the interaction ground state $|\Omega\rangle$ in terms of the free ...
- 838
3
votes
0
answers
151
views
LSZ reduction formula and connected Feynman diagrams in Peskin & Schroeder [duplicate]
I don't understand why in the LSZ reduction formula I need to consider only connected Feynman diagrams when I compute scattering amplitudes. From what I read in Peskin & Schroeder it seems that ...
- 357
2
votes
0
answers
77
views
LSZ theorem for trivial scattering
The $1\to1$ scattering amplitude is trivial and is given by (take massless scalars for simplicity)
$$
\tag{1}
\langle O(\vec{p}) O^\dagger(\vec{p}\,')\rangle = (2 | \vec{p}\,|) (2\pi)^{D-1} \delta^{(...
- 181
2
votes
0
answers
56
views
Conservation of angular momentum in LSZ reduction formula
I recently solved a problem involving calculating an LSZ reduction formula for the decay of a polarized photon into two pions. Specifically, I wrote an expression for the matrix element $\langle p_+,...
- 31
1
vote
0
answers
187
views
Angular momentum and the $S$-matrix
I have been curious about the status of angular momentum in the context of the $S$-matrix and scattering amplitudes. In particular, if we pass to a classical scattering problem and imagine scattering ...
- 858
-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
1
vote
1
answer
181
views
Calculate first-order term of the $S$-matrix for the $\phi^{4}$ theory [closed]
Before I ask a question, I will start with a small introduction.
I want to evaluate the $S$-matrix order-by-order in an expansion in small $\lambda$ for a $2 \rightarrow 2$ scattering in $\phi^{4}$ ...
- 237
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
3
votes
1
answer
326
views
General interpretation of the poles of the propagator
I am somewhat familiar with the fact that the poles of the Feynman propagator in QFT give the momentum of particle states. I'm also familiar with the KL spectral representation in that context (See ...
- 4,827
1
vote
0
answers
47
views
How to apply multiple Klein-Gordon operators to products of propagators?
I have the 4-point correlation function for a scalar free field
$$
\langle{0} | T \phi_1 \phi_2 \phi_3 \phi_4 | 0 \rangle = -\left[ \Delta_F(x_1-x_2) \Delta_F(x_3-x_4) + \Delta_F(x_1-x_3) \Delta_F(x_2-...
- 601