All Questions
64
questions
2
votes
1
answer
98
views
Feynman diagrams in string theory
I am beginning to study string theory, I have a beginner level doubt:
If we consider a Feynman torus diagram in string theory, it is a worldsheet. What does it represent? Does it actually mean that in ...
- 306
2
votes
3
answers
112
views
How do vacuum bubbles "dress" terms in the $S$-matrix numerator?
I am self-studying QFT using the book "A modern introduction to quantum field theory" by Maggiore. On page 124-125 he's doing the calculation in the interaction picture for a process with ...
- 613
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
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
1
vote
2
answers
221
views
$S$-matrix from LSZ
Considering $2 \rightarrow 2$ scattering in $\phi^4$, this loop diagram gives a contribution of
$$\int{dx_{1}dx_{2}dy_{1}dy_{2}dk_{1}dk_2 dp_1 dp_2 dq_1 dq_2 e^{-ik_1 x_1}e^{-ik_2 x_2}e^{ip_1 y_1}e^{...
user310742
0
votes
0
answers
60
views
How diagrams with loop and several propagators contribute to $S$-matrix element?
I studied Feynman rules with Schwartz textbook and what caught my eye was diagrams such as second and third on this picture (diagrams to the second order of $g$ for $\mathcal{L} = \frac{g}{3!}\phi^3$ ...
2
votes
2
answers
185
views
Difference of decay amplitude and transition amplitude from initial to final state
In Zwiebachs "A First Course in String Theory" 2nd edition he states in chapter 25.2, that
"the amplitude for an initial state consisting of a $\phi$ particle to turn into a final ...
1
vote
0
answers
40
views
Prefactor to amplitude for massless fermions/massive bosons
I was reviewing some of my old notes and found this formula for a matrix elements between two states:
$$
<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
3
votes
0
answers
152
views
Finding the interaction vertices
Given a Lagrange density $$\mathcal{L} = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi - \frac{m^2}{2}\phi^2 - \frac{\lambda_3}{3!}\phi^3 - \frac{\lambda_4}{4!}\phi^4$$ where $\phi$ is a scalar field,...
- 298
1
vote
0
answers
74
views
Optical theorem for Feynman diagrams
I'm studying section 7.3 of Peskin and Schroeder. In the middle of page 232, the book says:
For our present purposes, let us define $M$ by the Feynman rules for perturbation theory. This allows us to ...
- 789
4
votes
1
answer
540
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
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:
$$S=1+\sum_{i=1}^\infty\frac{(-i/\hbar)^n}{n!}\int_{-\infty}^\infty...\int_{-\infty}^\infty T[...
- 789
0
votes
1
answer
121
views
Contraction with external legs in $S$-matrix
If we consider following $S-$matrix element:$$\left\langle\mathbf{p}_1 \mathbf{k}_2|T\{\phi(x_1) \phi(x_2)\}| 0\right\rangle_0 $$
where $\phi$ denote Klein-Gordon field, and apply the convention in ...
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