All Questions
75
questions
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
0
answers
152
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
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
$$
\langle{0} | T \phi_1 \phi_2 \phi_3 \phi_4 | 0 \rangle = -\left[ \Delta_F(x_1-x_2) \Delta_F(x_3-x_4) + \Delta_F(x_1-x_3) \Delta_F(x_2-...
- 601
17
votes
2
answers
1k
views
What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?
For background, I'm primarily a mathematics student, studying geometric Langlands and related areas. I've recently been trying to catch up on the vast amount of physics knowledge I'm lacking, but I've ...
- 171
1
vote
1
answer
112
views
How do we interpret disconnected diagrams in scattering theory?
It is apparent that disconnected diagram contributes additional delta functions to the corresponding matrix element. For example, we consider the scalar $\phi^3$ theory and the following $2\...
- 619
0
votes
1
answer
62
views
Simplify a vertex in the on-shell form
I am calculating with a vertex connecting a pion, delta and a nucleon. In general, the vertex is calculated as
$$ \Gamma_{\pi N \Delta, a}^{\mu} \sim \gamma^{\mu\nu\rho} (p_\pi)_{\nu}(p_\Delta)_\rho ...
- 55
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:
$$
<f|S|i>= \delta_{fi} + [(2\pi)^4 \delta^4(P_f - P_i) \prod_{ext. fermion}\left(\frac{m}{...
1
vote
1
answer
120
views
Understanding from $S$-Matrix to Feynman-Rules in scalar QFT [closed]
I am learning QFT at the moment and the process from defining the S-Matrix to deriving the feynman rules is in my opinion pretty complicated, since there are many different things to pay attention to. ...
- 505
4
votes
2
answers
161
views
Are amplitudes for inverse processes related to each other?
The (generalized) optical theorem is presented in the book of Peskin and Schroeder (An introduction to Quantum Field Theory - chapter 7-Radiative Corrections:Some Formal Developments) as follows
$-i (\...
4
votes
1
answer
172
views
How to obtain (interacting) time-ordered correlation functions from the S-matrix - reverse of the LSZ formula?
The LSZ formula shows how to obtain the S-matrix elements from the time-ordered correlation functions of the interacting fields.
I wonder if there is a reverse formula; that is, can we find the ...
- 1,669
4
votes
1
answer
541
views
LSZ reduction formula in Peskin and Schroeder: How do we see that disconnected diagrams have incorrect pole structure?
In derivation of the LSZ reduction formula in Peskin and Schroeder, on page 227, the book says
Let us analyze the relation between the diagrammatic expansion of the scalar field four-point function ...
- 789
1
vote
2
answers
302
views
Interaction Picture Ladder Operators vs Free Field Operators
Consider the case of an interacting scalar field theory with bare mass $m_0$. After having derived the LSZ reduction formula, all that is left is to compute the time ordered products of the Heisenberg ...
- 749
0
votes
2
answers
330
views
Peskin & Schroeder LSZ formula missing in- and out states
In Peskin and Schroeder the LSZ-formula is given as below where the states in the $S$-matrix element are fully interacting Heisenberg states.
$$\begin{array}{l}\prod_{1}^{n} \int d^{4} x_{i} e^{i p_{i}...
- 498
3
votes
1
answer
385
views
Weinberg, off the mass shell Feynman diagrams
In section 6.4 of Weinberg QFT, the book says on page 286:
It is important to also consider Feynman diagrams "off the mass shell", for which the external line energies like the energies ...
- 789
4
votes
1
answer
275
views
LSZ reduction formula vs Dyson's expansion
In quantum field theory, we have use perturbation series to compute the $S$-matrix elements. For example:
$$S=1+\sum_{i=1}^\infty\frac{(-i/\hbar)^n}{n!}\int_{-\infty}^\infty...\int_{-\infty}^\infty T[...
- 789