Questions tagged [feynman-diagrams]
A diagrammatic technique introduced by Richard Feynman to describe the quantum behaviour of subatomic particles and their interactions. Do not use for general questions on diagrams that are not of the Feynman kind.
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Understanding the symmetry factors in diagrammatic expansion
Consider the $\phi^4$ scalar field theory.
$$
\mathcal{L} = \frac{1}{2} (\partial_\mu \phi)(\partial^\mu \phi) - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{4!} \phi^4
$$
with the partition function,
$$
Z[...
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When can colour charge indices be equated?
I'm currently studying QFT and QCD for the first time and I have a question about the colour charge indices given below. I was asked the following question:
(a) Derive the Feynman rule for the 3-...
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Trouble Understanding Computation In Nucleon Scattering Example in David Tong Lecture Notes
I am struggling to understand the following computation from page 59 of Tong's QFT notes
http://www.damtp.cam.ac.uk/user/tong/qft.html
The expression
$$
(-ig)^{2} \int \frac{d^{4}k}{(2\pi)^{4}} \frac{...
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Branch cut of a one-loop bubble diagram after cutting a single propagator
I am trying to understand Cutkosky cutting rules and generalized unitarity. Consider the article https://arxiv.org/abs/0808.1446 by Arkani-Hamed, Cachazo & Kaplan. In chapter 5.1 equation 133, the ...
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How forces are mediated if virtual particles are only a mathematical artifacts? [duplicate]
I was reading this post, that discusses whether if virtual particles do exist; stating that they are only a mathematical artifact that arises from perturbation theory. My question is, if virtual ...
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Massless Sunset Diagram $\phi^4$ [closed]
I should compute an explicit calculation for the sunset diagram in massless $\phi^4$ theory.
The integral is $$-\lambda^2 \frac{1}{6} (\mu)^{2(4-d)}\int \frac{d^dk_1}{(2\pi)^d} \int \frac{d^dk_2}{(2\...
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LSZ reduction formula and connected Feynman diagrams in Peskin & Schroeder [duplicate]
I don't understand why in the LSZ reduction formula I need to consider only connected Feynman diagrams when I compute scattering amplitudes. From what I read in Peskin & Schroeder it seems that ...
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Feynman parameters for $n=3$
I proved the general formula for the Feynman parameters:
\begin{equation}
\frac{1}{P_1^{a_1}...P_n^{a_n}}=\frac{\Gamma(a_1+...+a_n)}{\Gamma(a_1)...\Gamma(a_n)}\int_0^1dx_1...dx_n\delta(1-x_1-...-x_n)\...
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2-loop correction to exact 3-point vertex in a complex scalar field theory with cubed interaction
I am a graduate student with 1 quarter of relativistic QFT at the level of Srednicki (covered up to Chapter 30 this Fall). This question is not in any book that I know off and it wasn't assigned as ...
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LSZ reduction formula valid for any type of observables?
P&S on page 213 arrive at the following identity for the two-point function (eq. 7.5)
$$\langle \Omega|\phi(x)\phi(y)|\Omega\rangle={\sum_{\lambda} \int \dfrac{d^4p}{(2\pi)^4}\dfrac{ie^{-ip.(x-y)}}...
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Subleading correction to the gluon propagator in large $N$ expansion
I was reading Callan, Coote and Gross' paper on 2-dimensional QCD, where they show that the model that 't Hooft proposes in his work indeed produces quark confinement. In section VIII, they analyze ...
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QED Feynman graph Coordinate space doubt
So I know that there are the Feynman rules to transform mathematical equation into graphs but to me it's not too much clear when I should draw the graph vertically or horizontally i.e. how I determine ...
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Questions about the treatment of anomalies
I was reading Schwartz's QFT book, and in Chapter 30, he introduces the calculations of anomalies by evaluating objects like $\partial_\mu\langle J^{\mu 5}J^\nu J^\alpha\rangle$, where $J^5$ is ...
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Miraculous cancellations in a-priori non-renormalizable theories
Einstein's gravity is non-renormalizable since its coupling constant in 4D (I would like to limit the discussion to 4D) has negative mass dimension of -2.
Nevertheles it has been hoped that -- may be ...
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feynman scalar integral with on-shell condition
There are many integration written down in the standard QFT textbooks for scalar integrals in the computation of matrix elements. For example, in Peskin and Schroeder, we see
$$\int \frac{d^d \ell_E}{(...
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Fourier transformation of $\log(\mathbf{q}^2)/\mathbf{q}^4$ in $d=3$
(Note: I posted the exact same question in the math StackExchange, but I am trying to get more people to view it (I posted it here: same question on math StackExchange). The Fourier transformation has ...
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External leg correction to 3-point QED Green's function
I am trying to calculate the following diagram to solve the Callan-Symanzik equation for the three-point Green's function (two massless fermions and a photon).
The counterterm to the photon ...
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How to determine the charge of a $W$ boson in a Feynman diagram?
As the title says, I am not sure in what situations there is a W$^+$ boson and when there is a W$^-$ boson. My lecturer explained to me that you can view it either as the $W$ boson supplying a charge ...
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Renormalization in $\lambda\phi^4$-theory: Why renormalize at one-loop instead of renormalizing at order of the coupling constant $\lambda$?
I am reading about one-loop renormalization in the $\lambda\phi^4$-theory. Instead of doing renormalization at order $\lambda$, why are we interested in renormalization at one-loop which contains both ...
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About On-shell subtraction and renormalization
I really want your help, i have tried to solve it for two days but I couldn’t, therefore if you could help me by giving guidance and hint, i really appreciate it.
My question is that how to perform ...
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Feynman diagrams in statistical physics
Feynman diagrams were, to my understanding, first developed in QED to calculate things such as scattering amplitudes and the running of the coupling constants.
They have later been adopted to ...
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Can Alpha Decays and Gamma Decays be expressed via Feynman Diagrams?
I just learnt about Feynman Diagrams, and I've been going through many examples to practice the reading of Feynman Diagrams myself. I have already found diagrams for Positron Emission, Electron ...
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Feynmann diagram for $W$ boson decay
So a $W^{-}$ boson decays into right-handed antineutrino and left-handed lepton with "wrong" helicity. I found that textbook explanation of that process involves lots of handwaving.
I am ...
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Feynman diagrams with no lines crossing
What does it mean when we say a feynman diagram has no lines crossing? What are some examples of diagrams with and without lines crossing?
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Getting equation (16.159) in Ashok Das' QFT textbook
I am having difficulty in getting equation (16.159), page 730, in the book "Lectures on Quantum Field Theory", 1st edition, by Ashok Das. (The equation and page number is slightly different ...
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Is the scalar-field Feynman propagator at the origin ($x=0$) equal to 1?
I was reading about Feynman rules for scalar field in $\phi^4$ theory in section 4.6, pages 113-114 of Peskin & Schroeder, and, calculating amplitudes for processes, the authors show that Feynman ...
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Inverse muon decay on Mandl shaw- Help on $W$ boson propagator
Hello, I cannot understand why here the other term of the propagator of $W$ boson $k^{\alpha} k^{\beta}/m_{W}^{2}$ is not present, and how/if this absence is linked to the fact that we neglect terms ...
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Vacuum polarization
Interaction vertex of QED are like:
\begin{equation}
e \bar{\psi} {A\mkern-9mu/} \psi
\end{equation}
But we can't write a vertex where a particle-antiparticle pair annihilates in just 1 photon, due to ...
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Drawing appropriate Feynman graphs
I have learned to compute the corresponding mathematical expressions for a Feynman graph, however, I am yet to conceive the idea of drawing them properly for example
describes the nucleon-antinucleon ...
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Wick Rotation vs Sokhotski-Plemeli Method to compute internal loop of Feynman correlators
When computing loop integrals in QFT, one often encounters integrals of the form
$$\int_{-\infty}^\infty\frac{dp^4}{(2\pi)^4}\frac{-i}{p^2+m^2-i\epsilon},$$ where we are in Minkowski space with metric ...
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One-loop potential correction in QED (Lamb shift)
Vacuum polarization 1-loop in QED gives another term in potential, named Lamb shift. Potential in terms of momentum $p^2$ is:
$$V(p^2)= \frac{e^4_R}{2\pi^2p^2} \int_0^1 x(1-x)\ln[1-\frac{p^2}{m^2}x(1-...
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Question on the $i\epsilon$ prescription
I am computing an amplitude in the Minkowski signature and after performing dimensional regularization (dim-reg), contracting a lot of indices, and simplifying into a few momentum integrals to expand ...
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Is it possible to expand the measure in dimensional regularization?
In the dimensional regularization scheme, four-dimensional integrals are analytically continued from their $d$-dimensional counterparts, i.e.,
$$\int d^4 x\, f(x) \longrightarrow d^d x\, f(x)\,, \tag{...
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Dimensional regularization order of integration
I simply have a question of which integration I should perform first. Consider the typical integral from some loop calculation that has had the Feynman-trick and the typical dim-reg procedure perform,
...
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Question about writing amplitude for electron vertex correction
In Peskin and Schroeder, they write down the amplitude for the following diagram as 6.38
Why does the propagator for the photon with momentum $q$ never show up in the amplitude? Why is it ignored?
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Broken symmetry and three-photon vertex
I know that loop-level three-photon vertex in QED is zero since the contribution from fermion and antifermion cancel each other.
Also, from what I know this has something to do with gauge invariance ...
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Feynman's rule for Green's function of particle in the external field and with interaction
I'm learning the quantum field theory for condensed matter systems, and I've just learnt about the single particle Green's function with interaction and its Feynman rule. But I met some problems when ...
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Twisting internal/external lines in Feynman diagrams. How does it result in different diagrams?
I'm following Griffiths' Introduction to Elementary Particles. To introduce the Feynman rules, he proposes ABC theory, where these three spin-$0$ particles interact through a fundamental vertex:
One ...
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How to obtain the amplitude for the leptonic pion decay?
Consider the leptonic decay of the pion
$$\pi^{+}\rightarrow l^{+}\nu_{l}$$
In my notes there's written that in order to compute the associated rate we can use the effective Lagrangian
$$\mathcal{L}^{\...
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How does $t$-channel for electron-electron scattering in $g\psi\bar{\psi}$ exist?
Considering the Yukawa interaction $-g\phi\bar{\psi}\psi$ and $e^{-}e^{-} \rightarrow e^{-}e^{-}$ scattering, the 2nd order term in the numerator of the gell man low formula is
$\frac{(-ig)^2}{2!}$ &...
user310742
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Path integral derivation of exact identity for bosonic field
Let $\eta(t)$ be a non-dynamical Euclidean Gaussian bosonic field with partition function
$$
Z=\int D[\eta]\exp\left(-\frac{1}{2\sigma^2}\int_0^t \mathrm{d}\tau\,\eta(\tau)^2\right)
$$
so that $\left\...
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Performing Feynman parameter integral [closed]
How can I evaluate this integral?$$\int_0^1\int_0^1\int_0^1\frac{z}{1-z}\delta(x+y+z-1)dxdydz$$ I am getting $2\ln2-1$, but the answer should be $\frac12$.
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Interaction of a scalar and real field in quantum field theory: Cancellation of tadpoles [closed]
I am currently studying QFT and came upon this question. We are dealing with a theory of a complex field $\phi$ and a real field $\chi$. The interaction Lagrangian density is given by:
$${\cal L}_{\rm ...
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Pedagogic Notes on graviton self-energy 1-loop Calculation
Any lecture notes on graviton self-energy 1-loop calculation would be appreciated.
A detailed account of how to calculate the vertices of three gravitons, how to assign the momenta with signs to the ...
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Odd number of momentum should vanish but doesn't? [closed]
I have the following integral found within a loop-calculation (the actual content of the Feyman diagram, this is purely a math question)
\begin{equation}
J_\mu = \int\frac{d^4l}{(2\pi)^4}\frac{l_\mu}{...
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Derivation of Feynman rules in many-body theory
In textbooks on many-body quantum physics (e.g. Fetter and Walecka), Feynman diagrams are typically introduced after formulating the Dyson perturbative expansion of the Green's function using Wicks ...
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Loop diagrams with derivative couplings
Consider the following Lagrangian of two massless scalars in 3+1D interacting through derivative interaction:
$$
{\scr L} = \frac12(\partial a)^2(1 + g b) + \frac12(\partial b)^2,
$$
where $g$ is a ...
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How to recognize Feynman diagrams from the $S$-matrix expansion?
I'm studying scattering processes in QED and one usually have to compute first of all the Scattering matrix
$$\hat{S}=T\biggl (\exp\{-i\int d^{4}x:\bar{\psi}(x)\gamma_{\mu}\hat{A}^{\mu}(x)\hat{\psi}(x)...
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Meaning of a Feynman diagram in proof of Ward-Takahashi identity in chapter 7 of Peskin and Schroeder
I'm trying to understand what the external photon in this diagram (page 238 in P&S) corresponds to exactly. This diagram is supposed to be a contribution to the Fourier transform of a QED ...
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2
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Expanding functions with poles in QFT Calculation
I am using Series function in Mathematica on $(1/z)(-k^2)^z$. Up to $z^0$, the function gives me $1/z + \log[-k^2]$. But in the standard textbook on QFT, it turns out the expansion should give $1/z + \...
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