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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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Effective field Theory and Rayleigh scattering

I read a story somewhere that Feynman had the habit of asking unusual questions to the students during interviews. The two most famous of them are: 1) Explain why the sky is blue using methods of ...
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51 views

Possible infinite Feynman diagram question

This question came from a sci-fi show(refer to tagged link->EPISODE QUESTIONS-Physics Bowl). It seems like a Feynman diagram requiring path integrals. Can anybody solve it with a detailed step-by-...
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1answer
33 views

Imaginary part of vacuum polarization tensor

I deal with vacuum polarization diagram calculation with help of QED by Landau et al. and I would like to understand one interesting statement. I know how to compute $\Pi_{\mu\nu}(k)$ via dimensional ...
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1answer
40 views

How to know what type of diagram contributes to a two-to-two process?

There are 3 types of diagrams that can contribute to a two-to-two process; the $s$-channel, $u$-channel and $t$-channel. How do I know what diagrams can contribute to a process? I know that in QED, ...
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1answer
29 views

Cutkosky's rule for vertex correction

I don't understand how to evaluate the diagram for electron-photon vertex with help of Cutosky's rule: According to the rule, one should cut diagram "in the middle". I denote final state as F and ...
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How to determine the squared average amplitude for $\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$?

I have the following charged current interaction, at quark level, by the process: $$\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$$ By assuming that the energy is such that I can neglect the lepton and ...
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1answer
47 views

Superficial degree of divergence in $\lambda\phi^4$

Ryder at the beginning of the chapter about renormalization defines the "superficial degree of divergence" of diagrams in $\lambda \phi^4$ theory. I'll recap the derivation. A diagram in $\lambda\phi^...
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1answer
48 views

Sign ambiguity when going from position to momentum space evaluating Feynman diagrams

When calculating a simple diagram I came across an ambiguity in the conservation of momentum, i.e. it seems to me that the particle could come out of the process with opposite momentum with respect to ...
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1answer
34 views

Manipulation of momentum factors in Feynman integrals (solved)

My current understanding: Consider a massless Feynman graph with propagators of the form $1/p^2$ and some momentum factors in the numerator. Now consider a vertex, which for simplicity of notation is ...
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1answer
38 views

Higgs Feynman Diagrams

We have been told to compute the amplitude of these diagrams: I am struggeling with some basic points( I've only computed QED diagrams such as Bhabha scattering). Do you use $\epsilon$ for the ...
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1answer
21 views

Muon neutrino interacting with nucleon's quarks

I'm considering the muon neutrino/anti-quark interaction with the nucleons of ice in the IceCube experiment. The purpose is to decide which antiquarks are $\bar{q}$ and $\bar{q}'$. I have the ...
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0answers
48 views

Meson scattering amplitude in the linear sigma model

I am trying to calculate scattering amplitudes with linear sigma model Lagrangian, given as $$\mathcal L= \frac{1}{2}(\partial_{\mu}\sigma)^2+\frac{1}{2}(\partial_{\mu}\vec{\pi})^2-\mathcal U(\sigma,\...
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1answer
36 views

Propagator for W boson

I've found in different literature that some write the propagator for the W boson as $\frac{g_{\mu\nu}-\frac{k_\mu k_\nu}{M^2_W}}{k^2-M^2_W+iM_W\Gamma_W}$ and others like $\frac{g_{\mu\nu}-\frac{k_\mu ...
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1answer
26 views

Muon neutrino and down quark interaction diagram

My questions concerns the IceCube experiment, in particular, the interaction between muon neutrino and the down quark. I've drawn the following Feynman diagrams: Are both diagrams correct? Can I say ...
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2answers
82 views

Is this feynman diagram possible? $e^- + e^+ \to \nu_\mu + \bar{\nu}_\mu$

I am starting to learn about Feynman diagrams and I have been told that flavour has to be conserved at vertices in the case that the exchange particle was neutral. Since here the exchange particle is ...
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2answers
77 views

Could this feynmann diagram happen on its own? $e^- \to W^- + \nu_e$

I am starting to learn about Feynman diagrams and I wonder if this reaction could happen as a physical process on its own, as opposed to part of a more complicated diagram: $e^- \to W^- + \nu_e$ ...
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1answer
51 views

Completeness of an electron-electron-scattering in the Feynman diagram

During an electron-electron-scattering in any case the electrons change their directions and by this undergo accelerations. Shouldn’t the electrons emit photons in this time, loosing a part of its ...
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0answers
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An involved Feynman integral

Working with QCD, I have found the following integral from Feynman diagrams to solve $$ I(p)=\int\frac{d^4p_1}{(2\pi)^4}\int\frac{d^4p_2}{(2\pi)^4}\frac{1}{p_2^2-m_0^2} \left(\frac{p\cdot p_1-p_1\cdot ...
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0answers
38 views

Approximations in QFT and the problem of convergence

I would like to understand the problem of the convergence/divergence of the series appearing in QED: my question is inspired by a great article of John Baez, which can be found online. On the page 23 ...
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0answers
35 views

Feynman diagrams: How to find factors for external particles

In class we learned how to compute Feynman rules from the Lagrangian. I know how to find propagators and vertices. But is there a general rule for external particle lines?
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1answer
51 views

One-loop diagram in scalar field theory

We see that this loop contain particle with momentum $p+k$ and anti-particle with momentum $k$. But I fall into contradiction because the Feynman integral corresponds to this loop (see the book http:...
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2answers
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Lagrangian with quadratic interaction

A real scalar field has Lagrangian $L=L_0+L_1$, where the free part $$L_0=-\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2$$ and the interaction term $$L_1 = + \frac{1}{2}g\phi^2.$$ I have two ...
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Generating functional for amputated connected Green functions

As I understand, generating functional for amputated connected Green functions is exatly $\mathcal{S}$-matrix of theory. One can represent this functional as (for instance, $\phi^3$ theory): $$e^{\...
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0answers
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Is it possible to define Feynman diagrams in curved space-time?

I have a very simple question: "Is it possible to talk about Amplitudes and Feynman diagrams assuming a different background than the usual Minkowski one? Let's assume for example that the background ...
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One-loop correction to triple gluon vertex in QCD

I'm trying to calculate a one loop correction to the 3 gluon vertex, which is given by a circular correction, and another that's due to the 4 gluon vertex. However I'm unsure how the ghost fields ...
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1answer
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Can the Hermitian conjugate of a column vector still be column vector?

From what I understand, contravariant vectors are represented by column vectors, and covariant vectors are row vectors. So for a QED current, say $j ^ { \mu } = \overline { \psi } \gamma ^ { \mu } \...
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Feynman rule for 3-gluon vertex

I want to obtain the Feynman rule for the 3-gluon vertex, but looking at the result I don't really know how to tackle it. The relevant term in the Lagrangian is \begin{equation} \mathcal{L}_\text{...
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1answer
81 views

Compton Scattering Lowest Order Feyman Diagram

I have some trouble understanding the lowest order feyman diagrams for compton scattering. Does two feyman diagrams mean that compton scattering can happen through two processes? What is the ...
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2answers
66 views

Equivalence between $t$ and $u$ channels

Reading about QFT diagrams, I've seen examples like Bhabha scattering where the channel $u$ wasn't necessary due to the final states are distinguisable for being made of the different particles and ...
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1answer
51 views

Can a black hole ever be the output of a Feynman diagram in momentum space?

For a Feynman diagram representing a collision, particles come in from infinity with certain momenta, collide and then go off to infinite with other momenta. At collision vertices we integrate over ...
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1answer
94 views

Symmetry factor in $\phi^4$ theory

I'm having trouble while trying to understand what the symmetry factor of a Feynman diagram really is. From books I get that it is a geometrical factor that you get by the number of ways in which you ...
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Equations of Feynman Diagrams [closed]

How do you convert Feynman diagrams into equations? Is there something similar to chemical reaction equations? If so, how is it possible to solve for certain values or are there too many variables? ...
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Geometric series of two point function and self energy

This question is related to this question Proof of geometric series two-point function. Suppose we have a graph $A$ with a symmetry factor $s_1$. According to Srednicki (chapter 9, eq. (9.13)) for a ...
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1answer
121 views

Feynman Rules for Two Different Interacting Fields

I'm currently studying how to deduce Feynman rules for general theories, and I've managed to deduce them for $\phi^3$ and $\phi^4$ theories. Up to this point I've considered the same field for all ...
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1answer
67 views

Proof of geometric series two-point function

In deriving the expression for the exact propagator $$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$ for $\phi^4$ theory all books that i know use the following argument: $$G_c^{(2)}(x_1,x_2)=G_0^{(2)}...
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Propagator $K_F(x-x)$ in Feynman diagrams

Sorry for the elemental question, but this is a doubt that just struck me. I'm currently learning Feynman diagrams for different interacting theories (course bibliography is mostly Peskin and Greiner),...
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1answer
86 views

Definition of one particle irreducible diagrams

Text books often defines One-Particle Irreducible diagram (1PI diagram) as a connected diagram which does not fall into two pieces if you cut one internal line. Is this internal line the full ...
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1answer
95 views

How many counterterms does QED have?

I have read the statement that QED has four counterterms to cancel divergences. However, I have learnt that there are only three counterterms (vertex, electron propagator, photon propagator), which is ...
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1answer
60 views

Proof of 1-particle irreducible (1PI) diagrams

If we split the effective action into $$Γ[Φ] =\frac{1}2ΦiG_0^{-1}Φ + Γ^{int} [Φ]$$ we can show that the full propagator is given by $$G= i[iG − Σ]^{-1}$$ With $$Σ=-Γ_{ΦΦ}^{int} [Φ]$$ Here $Γ_{...
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2answers
52 views

Charged and neutral current in Feynman diagrams

I am stuck on finding the 'right' mediator in weak interactions. Consider the following reactions. 1: $$\mu^+\rightarrow \bar{\nu}_\mu + e^+ +\nu_e$$ This is mediated by the vector boson $W^+$. 2: ...
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0answers
44 views

Interaction Lagrangian for specific channels

I'm trying to build an interaction Lagrangian (${\cal L}_{int}$) with 2 fields, a complex $\varphi$ and another $\chi$ that can be real or complex. The key is to do it granting $U(1)$ symmetry and in ...
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1answer
179 views

Feynman rules out of the Lagrangian

Accordingly to chapter 10, section 10.6 Feynman Rules of 'Introduction to Elementary Particles' by David Griffiths, there is a way to extract the vertex and propagators just by inspection of the ...
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75 views

Question about Gluon self energy diagram/symmetry factor

I am a qft beginner and have a question: In Peskin & Schroeder chapter 16.5 there is given an expression for a gluon self energy diagram: According to the feynman rules we get $\frac{1}{2} \int \...
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1answer
56 views

Proof of overall momentum conservation

In $\phi^4$ momentum conservation at each vertex comes from integration in the vertex. How can from momentum conservation at each vertex proof overall momentum conservation that is if $k_1,k_2 ,k_3,...
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3answers
140 views

Feynman diagrams

Feynman diagrams are drawn on Space-time graphs. So is it possible for any particle path in that diagram to have a slope smaller than 45° or greater than 135°, i.e. can they travel faster than light? ...
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Mass insertions in Feynman diagrams

I'm trying to calculate some Feynman diagrams for $Z\rightarrow q\bar{q}$ at one-loop order in RPV SUSY with some $B$-violating vertices; these are triangle diagrams with 1-2 squark lines running in ...
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2answers
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How can I prove the annihilation electron positron can't generate positron + muon? [closed]

How can I prove the process $e^{+}+e^{-}\rightarrow e^{+}+\mu ^{-}$ doesn't happen?
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2answers
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Regularization: Evaluating the one-loop $\phi^4$ integral to order $\lambda^2$

I'm currently on the chapter of regularization on Zee's QFT book. For the $\phi^4$ theory, an amplitude for a single loop correction to order $\lambda^2$ is given by a diagram Following the Feynman ...
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0answers
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Easy way to extract UV divergence of an Feynman integral (1-loop, Dim-Reg)

For scalar integral (I mean Feynman integral with no numerator), using dimensional regularization, one could expand the integrand (treating the integration variable infinitely large) and calculate the ...
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0answers
52 views

Feynman rule for a vertex with spinorial structure

Consider the interaction term $$\mathcal{L}_{\rm{int}}=-g\bar\psi_1\gamma_\mu\psi_1 \bar\psi_2\gamma^\mu\psi_2,$$ where $\psi_i$ are fermions. I would like to calculate the Feynman rule for the vertex....