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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Confusion about the dressed propagator

When considering interactions, the free propagator $S_0(p)$ of fermions for example gets "dressed" due to the self-energy of the fermion. The complete propagator then becomes $$ S(p)=\frac{/\...
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Do quark self-energy insertions on external quark lines vanish in the MS scheme?

As far as I know, if one wishes to consider quark self energy diagrams inserted on external legs of a scattering amplitude, they cancel with the crossterm diagrams in the on-shell scheme. For this ...
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Next-to-leading $1/N$ contributions to Feynman diagrams in large $N$

I want to understand $1/N$ contributions to quark bilinear operators $J(x)$ in large $N$, for instance, operators of the form $q\bar{q}$ or $\bar{q}\gamma^\mu q$. As pointed out by E. Witten, in the ...
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What is the definition of the 0th element of the spin 1/2 four vector?

Is it: $$ S_\mu = (I, \frac{1}{2}\vec{\sigma})\quad\text{or}\quad S_\mu = (0, \frac{1}{2}\vec{\sigma}) $$ Specifically in the "CHIRAL DYNAMICS IN NUCLEONS AND NUCLEI" Bernard,Kaiser,Meißner, ...
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Correspondence between Feynman diagrams in the $n$-point correlation function expansions for 2 different cutoffs

My understanding of QFT is quite elementary. I'm reading through Kevin Costello's book on Renormalization and effective field theory, which is based on Wilsonian low energy theory. The integral for an ...
Yashasvi Aulak's user avatar
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4-graviton vertex of which one is an emitting graviton

For a four graviton vertex function, suppose $h_{\alpha\beta}h_{\gamma\delta}h_{\varepsilon\zeta}h_{00}$, of which $h_{00}$ is the emitting graviton to infinity. Now if we associate four-momenta $p_1$,...
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Interpreting Feynman diagram of Coulomb scattering of positron

I am trying to understand Coulomb positron scattering. This course explains that: Here the incoming state is in the future and is to be interpreted as a negative-energy electron of four-momentum $-...
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Deriving Feynman rules for scalar QED

I am a bit confused about Matthew D. Schwartz's statement of the Feynman rules in scalar QED (chapter 9, section 9.2 titled Feynman rules for scalar QED. The Lagrangian is \begin{equation} \mathcal{L} ...
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Feynman diagrams vs old fashioned peturbation theory (OFPT) vs reality

As far as I understand, our best picture of the world is that it is comprised of universe-spanning fields (one for each type of particle) that can interact with each other. The interactions are local, ...
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Are QED Feynman diagrams readable in any order?

I have somewhat of a basic question regarding QED Feynman diagrams. To expose my doubts let's take the Feynman diagram of the Compton scattering (at the second order) as an example: With the solid ...
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Why are two gluons needed for Feynman diagram?

Why do we need two gluons for the decay $$\pi^-+ p\rightarrow\pi^-+n+\pi^+\:\:?$$ If we have always the gluon $$\frac{1}{\sqrt{2}}(r\bar{r}-g\bar{g})$$ it should be possible with only one gluon ...
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Self-energy of a spinon coupled to a $\rm U(1)$ gauge field

I would like to understand how to calculate the 1-loop self-energy for spinons coupled to a $\rm U(1)$ gauge field. For context, I am going through Nagaosa & Lee's "Gauge theory of the normal ...
dumbpotato's user avatar
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Another Fourier transformation but with a $\sqrt{\mathbf{q}^2 + m^2}$ term now

Just as the title proclaims, I have a Fourier transformation I am trying to determine. Here is the Fourier transformation in its full form: \begin{equation} \int\frac{d^3q}{(2\pi)^3}e^{i\mathbf{q}\...
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Peskin and Schroeder page 201, solving integral over angular part

They make the following steps: $$\int\frac{\Omega_\bf{k}}{4\pi}\ \frac{1}{(\hat{k}\cdot p')(\hat{k}\cdot p)} = \int_0^1d\xi\int\frac{\Omega_\bf{k}}{4\pi}\frac{1}{(\xi\ \hat{k}\cdot p'+(1-\xi)\ \hat{k}\...
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Peskin and Schröeder page 195, IR divergence in the electron vertex function, rewriting integral

Peskin and Schröeder make the following statement $$\int_0^1dxdydz\ \delta(x+y+z-1)\frac{1-4z+z^2}{\Delta(q^2=0)}=\int_0^1dz\int_0^{1-z}dy\frac{-2+(1-z)(3-z)}{m^2(1-z)^2},\tag{p.195}$$ where $$\Delta =...
Jens Wagemaker's user avatar
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Coulomb potential from QFT in the external field approximation [closed]

In eq. (13.6.8) at page 558 of the first volume of the Quantum Theory of Fields by Weinberg, the following identity is given: \begin{align} \left[\frac{1}{(q_1\cdot p +i \varepsilon)((q_1+q_2)\cdot p +...
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Writing matrix elements according to Feynman rules and it's order

Let's say i want to calculate matrix elements for $e^+e^- -> \mu^+\mu^-$. Since interaction term is $\mathscr{L}_{int} = -ie\bar{\psi}\gamma^{\mu}\psi A_{\mu}$, as picture i'm adding shows(from P&...
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Energy Conservation in Pair Annihilation and Feynman-Stuckelberg Interpretation

The textbook "Modern Particle Physics" by Mark Thomson on p. (98) reads: In the left plot, an electron of energy $E$ emit a photon with energy $2E$ and, to conserve energy, produces an ...
Samama Fahim's user avatar
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Relative minus sign in $\gamma\gamma\to e^+e^-$ scattering

I need to compute the scattering amplitude for the process $\gamma\gamma\to e^+e^-$ at tree-level in QED. In my notes, it is written that there are two Feynman diagrams for this process, but I only ...
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Diagrammatic derivation of the Dyson–Schwinger equation

I am following chapter 9 of the Rammer's book on Field Theory (which you can find here: https://www-thphys.physics.ox.ac.uk/talks/CMTjournalclub/sources/Rammer.pdf). I am referring to section 9.2.2, ...
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Issue in Feynman propagator with derivative of a scalar field: which Feynman rule do I apply?

While solving a QFT exercise, I'm trying to calculate the Feynman propagator $$ \underbrace{\partial_\mu \phi(x) \phi(y)} = \langle 0 \vert T { \partial_\mu \phi(x)\phi(y) } \vert 0\rangle $$ where ...
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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)\...
Alex's user avatar
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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 ...
Lip's user avatar
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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}{(...
Quantization's user avatar
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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 ...
lain's user avatar
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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 ...
Solidification's user avatar
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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 ...
A22MS's user avatar
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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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