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3
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0answers
37 views

how to construct self-energie diagrams

I am working on self-energie and feynmann diagrams. they are not very easy to get but i think i am starting to understand how it works but of course i am not realy sure.and before going any further i ...
4
votes
1answer
51 views

Superficial degree of divergence on Weinberg

Reading volume 1 of Weinberg's QFT book, chapter 12, page 505 he says that if you consider a diagram with degree of divergence $D\geq{}0$, its contribution can written as a polynomial of order $D$ in ...
3
votes
2answers
91 views

Feynman diagram, which virtual particle?

Hi I have been asked to produce the lowest order Feynman diagram for the following scattering process: $$a.~~~ \mu^-+\mu^-\rightarrow \mu^-+\mu^-$$ $$b.~~~ \mu^-+\mu^+\rightarrow \mu^-+\mu^+$$ The ...
0
votes
0answers
46 views

What is a Witten diagram?

Recently I heard the terminology of Witten diagram. Studying QFT, I frequently see Feynman diagrams and use them to compute scattering amplitudes, one-loop corrections and so on. In string theory ...
1
vote
0answers
15 views

Fermion decay into axions

Do you know any literature on fermion decay into an axion and a lighter fermion? I am especially interested in the dependence of the decay width on the initial fermion momentum. The momentum should ...
0
votes
0answers
36 views

Help in writing down Feynman rule? [duplicate]

I have a term in my Lagrangian that looks like: $A^\mu B^{*\nu} \partial_\mu B_\nu - A^\nu B^{* \mu} \partial_\mu B_\nu$ where A is the photon field, and B is a charged, massive spin-1 boson. I am ...
1
vote
0answers
34 views

Creation of momentum on vertex (quantum field theory)

For a an interaction term like $g(\overline{\psi} \gamma^\mu \psi) \partial_\mu \phi$ in which $\psi$ is a Dirac spinor and $\phi$ a scalar field (d=4), should we expect this vertex to have a momentum ...
2
votes
0answers
93 views

What prevents this third-order QED scattering from having a non-zero amplitude?

I have learned that in the Dyson-Wick expansion of the QED scattering operator $$ S=e^{-i\int_{t_i}^{t_f}H\mathrm{d}t} $$ with the QED interaction Lagrangian $$ H=e\bar\psi\gamma^\mu A_\mu\psi $$ ...
1
vote
0answers
61 views

Does this vertex equal 0?

If I have an interaction term in my Lagrangian that looks like: $\mathcal{L}_{int} = (\partial_\mu B_\nu)(A^\mu B^\nu - A^\nu B^\mu)$ where B is a massive spin-1 field. Am I correct in thinking that ...
3
votes
0answers
45 views

Calculation of divergences of Feynman diagram

In Peskin Schroeder, while considering gluon diagrams for $\beta$-function in QCD, they say that we can calculate the divergent part of loop diagram taking limit of zero external momenta - e.g. for ...
2
votes
0answers
49 views

Creation / annihilation and Higgs mechanism representations

a silly question about the Feynmann diagrams of matter creation / annihilation In this Electron–positron annihilation , the Higgs mechanism steps in 3 times : after the electronic pair , before the ...
0
votes
0answers
44 views

Is the Symmetry factor different in Path integral Formalism?

Is the Symmetry factor different in Path integral Formalism and the Perturbation theory (canonical) formalism? For example, the order-1 4-point cross X diagram in the $\phi^4$ theory has symmetry ...
2
votes
0answers
161 views

What is the effective (quantum) lagrangian of a fermion field for fixed electromagnetic field?

... or, put it another way, what are the loop corrections to the dirac equation in the presence of a fixed (external) electromagnetic field?. Background Let $\mathcal ...
1
vote
0answers
61 views

Propagator with derivative interaction

I work with this interaction Lagrangian density $$\mathcal{L}_{int} = \mathcal{L}_{int}^{(1)} + \mathcal{L}_{int}^{(2)} + {\mathcal{L}_{int}^{(2)}}^\dagger = ia\bar{\Psi}\gamma^\mu\Psi Z_\mu ...
1
vote
1answer
32 views

QCD-Process with superposition-particle

I am a total beginner with non-abelian gauges. To write down a process from a neutral pion ($\pi^0 = \frac{1}{\sqrt{2}}(u\overline{u}-d\overline{d})$) I expect to have to write it as this ...
1
vote
0answers
51 views

Why can a left handed fermion transform into a right handed fermion and vice versa? [closed]

How (mathematically) can we show a left handed fermion turning into a right handed fermion?
1
vote
0answers
64 views

Question about interacting fields and feynman diagrams [closed]

The picture is taken from Chapter 4: 'Interacting Fields and Feynman Diagrams in An Introduction to Quantum Field Theory by Peskin and Schroeder. There is a two point correlation function ...
4
votes
1answer
152 views

Symmetry factor for Feynman diagrams in $\phi^4$-theory for $n$-points Green function

I'm working with two theories. Theory A: $H_{int} =\int d^3x \frac{Mg}{2}\phi\varphi^2$ Theory B: $\phi^4$-interaction: $H_{int} = \int d^3 x \frac{\lambda}{4!}\phi(x)^4$ Where $M$ is the mass ...
2
votes
0answers
83 views

Feynman amplitude for electron-positron annihilation and $W^{\pm}$ production

I'm working with this interaction Hamiltonian density $$ H_{int}(x) = ig\bar{\Psi}_{\nu_e}(x)\gamma^\rho P_L \Psi_e(x)V_\rho(x) + igV^\dagger_\rho(x)\bar{\Psi}_e(x)\gamma^\rho P_L \Psi_{\nu_e} $$ ...
0
votes
2answers
70 views

Momentum conservation in the one-loop contribution of the photon propagator

The lowest contribution to the photon self-energy is represented by the following diagram (Taken from F.Schwabl, Advanced quantum mechanics, p.365):: ($k$ is the momentum of the photon that decays in ...
1
vote
0answers
58 views

How does one calculate Feynman rules from a given lagrangian in QED?

I am a beginner in learning QFT. In homework problems in QED I often meet questions that asks one to calculate Feynman rules from some given lagrangian density. Some simple idea is to "read off" the ...
0
votes
1answer
76 views

Why four-point vertex function in $\phi^3$ theory?

So as I understand it the order of $\phi$ in a scalar Quantum field theory is indicative of the number of lines entering a given vertex. For example for $\phi^3$ this leads to vertices like the one ...
1
vote
0answers
56 views

How do I decide when to use raised/lowered indices when calculating the amplitude of a Feynman diagram?

I am learning the Feynman rules for QCD. The book I am reading tells me that gluon propagators contribute a factor of $$\frac{-ig_{\mu\nu}\delta^{\alpha\beta}}{q^2}$$ However, in one of the ...
0
votes
0answers
19 views

derivation of formula for number of closed loops in a Feynman diagram [duplicate]

How does one derive the formula $$V=I-L+1$$ where $V$=No. of vertices, $I$= No. of internal lines and $L$=No. of closed loops. I've seen it stated in several lecture notes on QFT but none (that I ...
0
votes
0answers
28 views

Feynman diagrams with ghosts and symmetry breaking

Let us think of an abelian gauge theory, precisely a scalar QED with 3 complex components of the scalar field and a 4-degree auto-interaction mixing components. Let us consider a spontaneously ...
2
votes
0answers
47 views

Why is the D0 oscillation so different from the K0 and B0?

I have looked for this answer into many articles and books but I am not able to figure out why $D^0\to\bar{D}^0$ is so highly suppressed if compared to the $B^0 \to \bar{B}^0$ and $K^0 \to \bar{K}^0$ ...
3
votes
1answer
102 views

How does order of scalar $\phi$ interaction impact feynman diagrams?

On page 60 of srednicki (72 for online version) for the $\phi^{3}$ interaction for scalar fields he defines $Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta ...
3
votes
1answer
84 views

Tadpole diagram in QED

In $\phi^4$ theory with the $\lambda \phi^4 / 4!$ interaction term gives rise to “tadpole” diagrams like this: If I have a standard QED interaction with $e \bar\psi \gamma^\mu \psi A_\mu$, can I ...
1
vote
0answers
38 views

QFT decay rates in lower dimensions

My starting point is the decay of a Higgs particle into two fermions, with decay rate proportional to \begin{equation} \Gamma \propto g_\psi^2 N m, \end{equation} where $g_\psi$ is the coupling, $N$ ...
2
votes
0answers
97 views

Number of distinct Feynman Diagrams for different orders of $\phi^4$ theory for 2 point function

There is 1 distinct Feynman diagram for zeroth order and 2 distinct diagrams for first order in $\phi^4$ theory for two point function. I want to know is there a way to predict the number of distinct ...
2
votes
0answers
78 views

Is this an error in A.Zee's 《Quantum Field Theory in a Nutshell》?

I am reading A.Zee's 《Quantum Field Theory in a Nutshell》 page 44. He is trying to evaluate $Z(J)=\int_{-\infty}^{+\infty}dq e^{-\frac{1}{2m^{2}}q^{2}-\frac{\lambda}{4!}q^{4}+Jq}$ Of the term ...
0
votes
0answers
92 views

How do I get the amplitude for the one-loop photon self-energy?

I am studying Maggiore's book on QFT and I am stuck in the amplitudes of one-loop corrections in QED. Could someone clearly explain me how do I get the following amplitude from the respective diagram? ...
1
vote
0answers
40 views

Combinatorics of fourth order feynman diagram

I am trying to calculate how many different forth order feynman loop diagrams I can produce. I know that for 2nd order it is 6x3x2 thus 3! since you start with 3 lines coming out of each vertex so 6 ...
0
votes
0answers
56 views

Propagator for fermion fields and Feynman diagrams

I need some help concerning the interpretation of propagators and Feynman diagrams. The free fermion propagator is given by the contraction of two fields $\psi(x),\bar\psi(y)$: ...
3
votes
2answers
114 views

Feynman diagram for attractive forces

I’m looking at Feynman diagrams for attractive forces and I'm thoroughly confused. Below are three diagrams from HyperPhysics: These all illustrate instances where the forces are attractive. ...
0
votes
0answers
85 views

u-Channel Matrix element for electron-positron annihilation

This one is a quantum related question. The calculation relates to the Matrix element for the annhilation of a electron-positron into two photons: $$ e^-e^+\rightarrow\gamma\gamma $$ I've recently ...
0
votes
1answer
87 views

Is a Feynman diagram depicting a vacuum bubble “that gets real” valid?

In exercise I.7.3 of A. Zee's QFT in a Nutshell, we have to draw all the Feynman diagrams of the scalar theory $$ Z(J) = \int D\varphi e^{i\int d^4x\{\frac ...
2
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0answers
34 views

Is this the correct way to obtain $<f|i>$ term in $\phi^4$ interaction theory? [closed]

Lets first write the expectation value of the fields in the interaction picture; $$ ...
0
votes
1answer
36 views

What does “n-particle reducible” mean?

I am reading Ramond and in page 112 he says "In $\lambda \phi^{4}$ theory, diagrams can be at most three-particle reducible". My question: whether the individual Feynman Diagrams are treated as ...
0
votes
0answers
16 views

IBP Identities to solve differential equation

I am wondering if anyone has experience in using IBP( Integration by parts) identities in the evaluation of Feynman diagrams via differential equations? My question is that I can't seem to understand ...
0
votes
1answer
60 views

Photon-Photon-scattering (Feynman diagram)

The feynman diagram for the Delbrück-scattering (photon-photon-scattering) in the lowest order looks like as in the picture: But why is the following diagram equal to one of the upper three? There ...
1
vote
1answer
104 views

Zee's Nutshell: Feynman diagrams “baby problem”: Connected vs. Disconnected

On page 47 of A. Zee's QFT in a Nutshell, he explains how disconnected Feynman diagrams can be built from lower-order connected diagrams: I don't know how to understand formula $(6)$. I understand ...
0
votes
0answers
50 views

Mass term in field Lagrangian

In the Klein-Gordon or in the Dirac Lagrangian density, the mass term is quadratic in the field. The other way around, I have heard a quadratic term in a general Lagrangian density be referred to as a ...
2
votes
1answer
61 views

Feynman diagrams and gluon collisions/interactions?

We have been given this question which essentially asks us to draw the lowest order Feynman diagrams for various processes. One of them is: $$ g + g \rightarrow \bar{t}+t $$ Now, I am not an expert ...
0
votes
0answers
120 views

Feynman Diagrams Integral Calculation

Are there any easy tricks to calculate integrals of the form: $$\int d^4x \ e^{ikx} \dfrac{1}{x^2} \ \ (\text{ans:} \ i\dfrac{4\pi^4}{k^2}) \ \ \text{and} \ \ \int d^4x \ \mu^2 \dfrac{\ln ...
0
votes
0answers
65 views

How are tree-level calculations related to the classical theory?

I've read the answers (and linked notes) to another question (Tree level QFT and classical fields/particles) and I understand them. They seem to explain how to organise a perturbative calculation of ...
1
vote
1answer
68 views

How to derive the vertex factor for the four-field interaction in scalar QED?

I tried to find the Feynman rules using path integral. For scalar QED, I have an interaction term $e^2\phi^{\star}A_{\mu}^2\phi$. Generating function then can be written as $$ ...
1
vote
0answers
57 views

How do I derive Feynman rules for vectors involving derivatives?

Suppose I have a term in the Lagrangian: $$\cal{L} \equiv (\partial_\mu B^+_\nu) B^{-\mu} A^\nu $$, where $B^\pm$ are charged massive vector particles and $A$ is photon. Now, how can we derive the ...
5
votes
1answer
194 views

Scattering Amplitudes from Feynman Diagrams (Spinor Helicity Formalism)

$\require{cancel}$ I am trying to do an exercise from Scattering Amplitudes By Elvang (Exercise 2.9) which states: Show that $A_5(f^-\bar{f}^-\phi\phi\phi) = g^3\frac{[12][34]^2}{[13][14][23][24]} ...
1
vote
1answer
153 views

Feynman Diagrams for Yukawa Theory

I am trying to draw the Feynman diagram for the following scattering amplitude (f a fermion) $$ i\mathcal{M}(f\overline{f}\phi\phi\phi) $$ Given the following interaction term in the Lagrangian: $$ ...