All Questions
19
questions
-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
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
206
views
Calculating a four-point Green function using Wick's theorem (problem 12.1 in Mandl & Shaw)
In problem 12.1 in Quantum Field Theory, Mandl & Shaw the aim is to calculate the four point green function
$$ G^{\mu\nu}(x,y,z,w) = \frac{\langle 0 | T\big(A^{\mu}A^{\nu}\psi(z)\bar{\psi}(w)S\big)...
- 311
2
votes
1
answer
384
views
The relation between full Green's function and S-matrix
I'm learning Green's function in condensed matter. The full Green's function is defined as
$$G(k_2,t_2;k_1,t_1) = \langle\Omega |T a_{k_1}(t_1)a_{k_2}^{\dagger}(t_2) |\Omega \rangle $$
The $\Omega$ is ...
- 169
4
votes
1
answer
815
views
Why does a pole in the Green function correspond to a bound state?
Consider the many-body (zero temperature) fermion Green function
$$
G(a,b;t)=-i\theta(t)\langle\psi_a(t)\psi_b^\dagger\rangle
$$
Where I'm restricting $t>0$ for causality and that the free ...
- 2,123
4
votes
0
answers
97
views
Is crossing symmetry reliant on using the Feynman propagator?
If one used the advanced or retarded propagator instead of the Feynman propagator would crossing symmetry necessarily be violated in some scattering amplitudes?
- 2,270
5
votes
1
answer
769
views
LSZ formula and connected Green functions
My question is relatively simple. In the LSZ formalism, it is said that S-matrix elements correspond to on-shell limits of Green's functions. On the other hand, what people usually do is that they ...
- 325
1
vote
0
answers
159
views
Connected part of $S$-matrix generating functional
I am currently studying an article by A.Jevicki et. al. (https://doi.org/10.1103/PhysRevD.37.1485) and I am a little confused. They say that the generating functional of the $S$-matrix is related to ...
- 93
1
vote
0
answers
154
views
Connected diagrams and Keldysh
I have seen that:
In the ground state ($T = 0$) formulation of the Green’s function written in terms of operators
in the interaction picture, the Green’s function reads:
$$G(r,t;r',t') = -i\frac{\...
user284619
0
votes
1
answer
73
views
Evaluation of transition amplitude between two field configurations
Consider a field theory of a scalar field $\phi$ described by an action $\mathcal{S[\phi]}$. Is there a way to determine the transition amplitude $\langle \phi(x,t)'|\phi(x,0)\rangle$?
1
vote
0
answers
979
views
S-matrix and Green's function
I'm considering one paper about electron recombination and there is an expression for S-matrix that confuses me
$${S_{fi}} = i\mathop {\lim }\limits_{t' \to \infty \atop t \to - \infty } \left\langle ...
- 258
3
votes
1
answer
253
views
Why do particle resonances lead to peaks in the cross section?
Since bound states lead to poles in Green functions, I wonder if this is the reason for peaks in the cross section.
From a QFT point of view, the infinitesimal cross section $\text d\sigma/\text d\...
- 2,648
2
votes
0
answers
148
views
Physical meaning of $\langle 0|S(+\infty,-\infty)|0 \rangle$
when I am reading text book Introduction to Many body physics Piers Coleman 2nd editor, Equation (5.26). I got confused about the meaning of $\langle0|S(+\infty,-\infty)|0\rangle$.
first problem
$|...
- 1,113
4
votes
1
answer
875
views
Why is the S-Matrix element essentially the residue of the Green function (LSZ formula)?
On Wikipedia, quite similar to the script I am following the LSZ formula is given as
$$
_{out}\left<p_1,...,p_n| q_1,...,q_m \right>_{in} =\\
\int \prod_i^m \left(\textrm{d}x^4\, i e^{-q_ix_i}(\...
- 103
7
votes
2
answers
1k
views
Physical poles in QFT scattering amplitudes?
In QFT, for instance in $\phi^3$ theory, the scattering amplitudes are said to be constrained to feature so called "physical poles" only.
Consider generalized Mandelstam variables
$$s_{ij},s_{ijk},s_{...
- 1,517