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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111 views

Do bubble/vacuum diagrams have some physical implication?

While calculating S-matrix elements $$\langle\Omega|T \{ \phi(x_1)...\phi(x_n) \}|\Omega\rangle=\frac{\langle0|T \Big\{ \phi_0(x_1)...\phi_0(x_n) e^{i\int d^4x\mathcal{L}_{i}[\phi_0]}\Big\}|0\rangle}{\...
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About a Feynman diagram of the fourth-order for the Compton scattering

I have been able to draw 16 of them. But I was not able to find the last one. It is told in the problem that there are 17 of them. So I had to check the solution and I find this diagram; At the same ...
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How can renormalised constants and perturbation expansions both be valid?

When we compute expectation values in QFT we use feynman diagrams/perturbation expansion. However, this requires the coupling constant to be small, however, when we renormalize we end up with ...
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Deep inelastic scattering (DIS) and handbag diagram

Here, in page 11, you can see the so-called 'handbag' diagram that explains how a virtual photon emitted in a deep inelastic scattering (DIS) process interacts with a parton. I'm going to use this ...
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Deriving Feynman Rule from lagrangian for Dirac fermions with explicit charge conjugation

I understand that there are several complications in dealing with fermion number violating interactions, for instance the fact that there is no unambiguous way to define a fermion flow arrow, but I ...
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4-fermion interaction - vertices calculation with Feynrules

Dear Feynrules users and all physics enthusiasts, I was going to derive the 4-fermion vertices in Feynrules and to pass the generated model further to MadGraph and/or CalcHep. According to the most ...
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Vertex Feynman rules for $ZZH$ coupling

I have a Lagrangian term $$\mathcal{L}=gHZ_{\mu \nu} Z^{\mu \nu}.$$ Where $$Z_{\mu \nu}={\partial}_\mu Z_\nu - {\partial}_\nu Z_\mu.$$ For this interaction, vertex Feynman rule is $$g (g^{\mu \nu}p.q -...
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Some questions about Feynman Diagrams

I have a few simple questions about Feynman Diagrams: Why, when $W^+$ or $W^-$ bosons are involved, sometimes the sign + or - is shown and sometimes not (example1, example2)? Why the arrow is usually ...
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Feynman rules: Difference between vector-scalar-scalar and vector-fermion-fermion vertex

I'm trying to understand the difference in cross section between top-quark pair production and pair production of scalar top quarks (top squarks) as predicted by Supersymmetry. Assume the mass of the ...
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Plugging the Fermi-Dirac distribution into the integral of a Feynman diagram

In this paper https://arxiv.org/abs/1211.6442 they compute the stress-stress correlation function for a Chern insulator by using a Feynman diagram with a Fermi loop and an ingoing and outgoing "...
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$\phi^4$-Theory: Sub-Diagram zero $\Rightarrow$ Diagram zero?

Considering a bosonic $\phi^4$-theory: If I know that a certain connected Feynman diagram has a vanishing contribution. Does this imply that all larger connected diagrams containing this diagram are ...
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Which QFT vertex will cause an electron to scatter off a spin-0 charged particle electromagnetically?

I am working through an exercise in QED from Halzen and Martin's textbook Quarks and Leptons. For the QED scattering process $e^-(k)\mu^-(p)\to e^-(k')\mu^-(p')$, the absolute square of the Feynman ...
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How do you decide if a process has $s$ or $t$ channel Feynman diagram?

Without working with Lagrangian, how can one explain if we are dealing with $s$ or $t$ channel diagrams? For example, for $\rm e^+e^-\to\gamma\gamma$, I thought $s$-channel diagram, but the solutions ...
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Mass renormalization with counterterm for scalar field theory

Sidney coleman in his lecture 253a of QFT stated that " one-meson-to-one-meson S-matrix element, we should find it equal to 1" i.e $$\langle p'|S|p\rangle = (2\pi)^32E_p\delta^{(3)}(\vec{p}'-...
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Question about Green's functions in QFT

I have this generator $$ Z(J,\lambda)=\int D\varphi e^{ i\int \!d^4x\,\{ \frac{1}{2}[(\partial\varphi)^2-m^2\varphi^2 ]-\frac{\lambda}{4!} \varphi^4+J\varphi \} } .\tag{11} $$ Which I ...
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1answer
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Peskin & Schroeder's way of showing $Z_1=Z_2$ via integration by parts

I am trying to follow Peskin & Schroeder's textbook on Renormalization. I tried a few ways but this does not match with the textbook. First equation (10.43 )in Peskin is given \begin{align} \...
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4-point Green's function for mesons

Starting with $$ Z(J,\lambda)=\int D\varphi e^{ i\int \!d^4x\,\{ \frac{1}{2}[(\partial\varphi)^2-m^2\varphi^2 ]-\frac{\lambda}{4!} \varphi^4+J\varphi \} } . $$ I have a question about how ...
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How to know if two diagrams interfere?

Are there/in which situations do two Feynman diagrams not interfere (besides for kinematic reasons like well separated poles)? I have heard that there is a way to easily predict if two diagrams do ...
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$1/\epsilon $ poles order in dimensional regularization of $\dfrac{\lambda}{4!}\phi^4$ theory

I have to find the order of 1/ε poles in dimensional regularization of $\dfrac{\lambda}{4!}\phi^4$ theory. The Feynman integral is the following: \begin{equation} I(p)=-λ^6\int \frac{d^4p_1}{(2\pi)^4}\...
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$φ^3$ scalar field one-loop diagram calculation via dimensional regularization

I have been trying to understand how to compute the following loop diagram in $\frac{\lambda}{3!}\phi^3$ theory, with $m\neq0$ and I am not getting anywhere. From what I understood I am supposed to ...
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How perturbative string theory handles QED-like vertices?

Perhabs my perspective of string theory is wrong, but I have no idea how the following works: A string representing a single fermion (like an incoming electron) splits into an other fermionic (...
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265 views

Why the Feynman diagram with loops attached to external legs is irrelevant to the $T$-matrix?

Hello friends I was stumbled when I learnt the scattering theory from textbook titled "Quantum Field Theory for the Gifted Amateur", which has related the scattering probability to the ...
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Why are the propagators in old-fashioned QED oblique, while in modern QED they are horizontal (or vertical)?

In old-fashioned Quantum Electrodynamics, one can find diagrams such as these (probably Stückelberg was the first to use this notation, a kind of predecessor of Feynman diagrams): In modern QED this ...
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120 views

4-momentum conservation vertex-by-vertex in diagrams — reference with explicit statement

A friend of mine does not believe that four-momentum is conserved independently in each vertex of a Feynman-diagram; and, as a consequence, that propagators/virtual particles do not obey a dispersion ...
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Are there Feynman diagrams for dimension-6 operator?

This document https://arxiv.org/abs/1008.4884 presents in Tables 2 and 3 the mathematical expression of many dimension-6 operators, for example (just an example) The mathematical expression does not ...
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Getting wrong number of Wick contractions

Consider this lagrangian: $$\mathcal{L} = \dfrac{1}{2} (\partial_{\mu}\phi_{1})^2 + \dfrac{1}{2} (\partial_{\mu}\phi_{2})^2 + \dfrac{m^2}{2}(\phi_{1}^2 + \phi_{2}^2) + \dfrac{g}{4!}(\phi_{1}^4 + \phi_{...
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Simple Explanation for Feynman Diagrams

How would you explain the concept and applications of Feynman Diagrams to a high school kid?
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Relation between Green’s functions and connected Green’s functions [closed]

I attempt to understand the $0$-dimensional QFT from these QFT lecture notes by Ronald Kleiss from 2019. The author defines the generating function $Z(J)$ and its logarithm in the following way. $$Z(J)...
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Retarded vs Feynman Klein-Gordon Propagators

Although I follow all the manipulations -- Green's functions, choice of contour/i$\epsilon$ prescription, etc -- I seem to be struggling with too many trees. The forest remains blurry. In ...
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Why is QED renormalizable?

My understanding of renormalizability is that a theory is renormalizable if it the divergences in its amplitudes can be cancelled out by finitely many terms. I see that by adding counterterm (in the ...
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76 views

Why does the background field effective action generate only vacuum graphs?

I refer to LF Abbott's "Introduction to the background field method". The background field generating functional is $$ \tilde{Z}[J,\phi] = \int \mathcal{D}Q \exp i[S[Q+\phi] + J.Q], \text{ ...
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Dimensional regularization of Electron self-energy from Ryder's book

I am Studying Electron self-energy using Ryder's textbook, In page 334 we can see Defining $k'=k-pz$ and avoiding the term linear in $k'$(because it integrates to zero) gives \begin{equation} \Sigma(...
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1answer
149 views

Feynman rules for interactions with derivatives: How exactly do the momentum factors appear?

I know how to treat Feynman interactions without derivatives by Wick contraction. But now, take for example $$\mathcal{L}_{int}=\lambda \phi (\partial_{\mu}\phi)(\partial^{\mu}\phi).$$ Now many books ...
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1answer
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Why are loop-induced processes finite without counter terms?

When a process has no tree-level contribution to the amplitude but occurs e.g. at 1-loop level it is said to be loop-induced. One property of loop induced processes is when you calculate the amplitude ...
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Determining reduced graphs in perturbative QCD

I am reading "Foundations of perturbative QCD" by John Collins and I find it hard to determine the general form of reduced graphs (that is feynman graphs, where internal lines which do not ...
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205 views

How to compute the quantum effective action from 1PI Feynman diagrams?

On page 33 of these notes by David Skinner, it is claimed that [starting from a connected graph and removing the bridges] tells us how to compute $\Gamma(\Phi)$ perturbatively from the original ...
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67 views

How to verify my calculated amplitude under gauge invariance structure?

I calculated the Compton amplitude of three diagrams but how can I verify it under gauge invariance structure? $$ {\cal A} = 2 e^2 \left[ \frac{ p_3 \cdot \epsilon_1 p_2 \cdot \epsilon_4^* }{ p_2 \...
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Differences between Feynman diagrams

I'm reading Weinberg's paper on "Dynamics at Infinite Momentum" in which he proves a claim about the type of Feynman diagram that contributes finitely to the perturbation series and the type ...
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1answer
120 views

Question about renormalization parameter in Srednicki's book

In Chapter 9 in Quantum Field Theory written by Srednicki. This chapter discusses why $Z_{i}=1+O(g^{2})$ and $Y=O(g)$, given specific values of $m$, $g$, and normalization conditions $$\langle k|\phi(...
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65 views

T-Channel matrix element

I’ve been reading an article about the matrix element of the three different channels In Feynman diagrams and I saw this. My question is how did k^2 - m^2 ( part of the fermion propagator) become 2p2*...
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31 views

Probability for each momentum in one-loop diagram equal?

Why is the probability for each momentum in a loop (e.g. vacuum polarization) equal? Why has a infinite momentum the same probability to occur than a virtual particle with low moment. I know - these ...
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2answers
57 views

Feynman Diagrams: Fermionic Line orthogonal to Time Axis

Can someone explain the meaning of this fermionic segment that is orthogonal to the time axis? I am relatively new to Feynman diagrams and have so far only observed lines orthogonal to the time axis ...
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1answer
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Change of flavour in strong interactions?

Sorry if this question has been asked already but after researching I have found that quark flavour is not changed in the strong interaction. This confused me because how can a down and anti down ...
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Does this is an onshell propagator?

This image is from here (page 6-7). My question refers to Eq. 26 and 27 The denominator changed from $(p_1 -p_3)^2 - m^2$ to $p_3^2 - 2p_3p_1$. So they used $p_1^2 = m^2$. But I thought, this relation ...
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Scattering of electron anti-neutrino on hydrogen (Feyman diagram)

Does anyone have a reference how the (lowest-order) Feynman diagrams for the scattering of an electron anti-neutrino $\overline\nu_e$ on a hydrogen atom would look like? I'm a bit confused about the ...
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40 views

Confusion among channel $u$ and channel $t$ in exclusive reactions

In the this paper (https://arxiv.org/abs/1203.4392), on page 2 it is said that Since DVCS amplitude is symmetric under $s \leftrightarrow u$ channel crossing, the CFFs and $^{S}C^i_{\cdots}$ ...
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Summing over disconnected diagrams - Peskin and Schroeder

In Peskin & Schroeder, page 97, the following expression is given as part of the demonstration of how the $n$-point correlation function is calculated using connected diagrams: $$\sum_{\text{...
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QFT and coordinate transformations

I was going through this lecture, where Leonard Susskind explains that these two Feynman diagrams are considered to be equivalent in QFT: One diagram explains the same phenomena in one possible way ...

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