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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Two-loop integrals in particle physics: Odd number of momenta and tensor decomposition

I have two simple, maybe related questions about tensor integral decomposition in multi-loop integrals Odd number of loop momenta: In one loop integrals, this is always true $$ \int \frac{\text{d}^D ...
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Graviton Scalar interaction - Feynman rules

Having the interaction lagrangian for scattering between two scalars and the graviton $h$ \begin{equation} \mathcal{L}_{\phi \phi h}=\frac{\kappa}{2}\left(-\frac{1}{2} h_{\mu}^{\mu} \phi^{2} m^{2}+\...
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$φ^3$ theory: three-point, one-loop diagram ($D=4$)

I am attempting to calculate the one-loop diagram for the $φ^3$ three-point function, which is equal to (dropping a factor of $-i$): $$g^3 \int_E \frac{1}{(2 \pi )^4} \frac{1}{(k+q)^2+m^2} \frac{1}{(k-...
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BCS and Feynman Diagrams

I am currently studying the strong coupling theory (by Eliashberg) of superconductivity, which is derived by BCS by considering self-energy diagrams and the following interaction potential $$ V(q, i\...
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Diagrammatic representations of generating functionals $Z[J]$, $W[J]$, and $\Gamma[\varphi]$

The book Boulevard of Broken Symmetries by Adriaan Schakel gives an excellent, if not exceedingly brief, overview of the path integral approach to perturbation theory. In particular, pages 47-58 give ...
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1-loop 4-point Feynman diagrams of four-fermion interactions

Consider the Lagrangian $$\mathcal L = \bar\psi(i\gamma^\mu \partial_\mu -\sigma)\psi +\frac{c}{2}\bar\psi\psi\bar\psi\psi.$$ I would like to calculate the $4$-point fermion interaction amplitude to ...
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What are the Feynman rules for the spinor-helicity formalism?

If we do not work with helicity amplitudes, there are Feynman rules for the external legs of a Feynman diagram, i.e. $u_s(k),\overline{v}_s(k),\epsilon_r(k)$ for an incoming fermion, antifermion and ...
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Why does $k_\mu k_\nu \to k^2 \eta_{\mu\nu}/d$ work in QFT calculations?

When doing calculations of Feynman diagrams in QFT I've seen a trick used that goes something like this $$\int \frac{d^dk}{(2\pi)^d} \frac{k_\mu k_\nu}{f(k^2)}\quad\longrightarrow\quad\int \frac{d^dk}{...
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Intuition behind coupling and interaction terms in Lagrangian?

I'm reading through Srednicki's QFT book, and when we introduce external fields, we often multiply terms together to represent the coupling in our Lagrangian densities. My understanding of what ...
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Feynman rules for exchange graphs

I'm looking into second-order Feynman diagrams in QED and something is unclear to me regarding the existence of both a direct and exchange graph. The way I understand it is that there are two ways in ...
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Why does Feynman say the color of a photon is a property of the source?

Note:I am new to Path Integrals/Lagrangian QFT. In the following link, Feynman says that the color of a photon is a property of the source and that "Energy is already contained (in his Feynman ...
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How can I intuit all the Feynman diagrams from a given interaction?

Let's say I want to calculate all connected 1-loop 4-point Feynman diagrams for a given interaction (in my case, with both $\phi^3$ and $\phi^4$ terms). Is there a way to lay out all the possible ...
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Electromagnetism, linearity and Feynman diagrams [duplicate]

Currently I am reading Sean Carrol, general relativity. But a thing got me stuck in, I can't understand what he is talking about. We are discussing the introduction to Einstein field equation, so he ...
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Feynman Diagrams of Infinite Order

It is often the case that infinite objects exhibit properties that are not reflected in any finite object; the behavior of infinite groups are for example fundamentally different in a number of ...
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Feynman Diagram for $\tau^{-}\rightarrow \pi^{-}\pi^{0}\nu_{\tau}$?

The Feynman diagram for the decay $\tau^{-}\rightarrow \underbrace{\pi^{-}}_{= \bar{u}d}\nu_{\tau}$ is easy to draw: But how about the decay $\tau^{-}\rightarrow \underbrace{\pi^{0}}_{= \bar{u}u}\pi^{...
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Do Faddeev-Popov ghost contribute to vacuum polarisation?

I can imagine how one can draw a Feynman diagram for a boson self-energy with a ghost loop. My question is, shouldnt't the amplitude of that process be 0 as the ghosts are merely a mathematical tool?
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Avoiding unnecessary calculations when deriving Feynman rules

I'm trying to understand some principle behind deriving Feynman rules for QCD, i.e. avoid unnecessary calculations. Setup Assuming we have a gloun field $A_\mu^a$, fermion fields $\psi$ and ghosts $c^...
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Why do we need effective action $\Gamma$ given the connected generating functional $W$?

I have just learnt the path integral formalism in QFT, up to the point where we computed the generating functionals $\mathcal{Z}[J] := Z[J]/Z[0]$, $W[J]$, and $\Gamma[\varphi]$. Here $J(x)$ is the ...
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Can you generalize Feynman diagrams to 2-dimensional CW-complexes?

Feynman diagrams (for just a typical run-of-the-mill QFT) are graphs, and it recently occurred to me that that means they are 1-dimensional CW-complexes; in particular, they are connected 1-...
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1answer
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Why can we set the external momenta to zero while calculating the 1-loop correction to non-abelian theory coupling?

Refer to the second diagram in figure 73.2 on page 440 of Srednicki's Quantum Field Theory book. On page 441 he proceeds to calculate the amplitude and argues that since the divergent part is ...
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Question on how to actually use momentum space Feynman rules in $\phi^4$-theory

The momentum space Feynman rules state that we "integrate over all undetermined momenta" and "impose momentum conservation at each vertex". This is given for example on page 95 of ...
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Drawing Feynman diagrams including $\pi^0$-mesons

I am struggling with drawing a Feynman diagram for particle physics processes including $\pi^0$ mesons and hope you can help my clarifying my confusion. Take, for example, the following process $$D^+ \...
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Gauge invariance of loop Diagrams

Say we have a gauge-fixed QED Lagrangian: $$\mathcal{L} = - \frac{1}{4}{F}_{\mu\nu}F^{\mu\nu}+ \frac{1}{2a}\left(\partial_\mu A^\mu\right)^2+\bar\psi_1(i\gamma^\mu D_\mu - m_1)\psi_1.$$ My question ...
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Does a photon have an amplitude of motion at a speed less than the speed of light?

In the book QED: The Strange Theory of Light and Matter, Richard Feynman writes that for a photon there are nonzero amplitudes of motion with a speed that is greater or less than the speed of light. ...
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The ${\cal M}_{if}$ that appears in the Feynman diagrams - Are they probability ranges?

${\cal M}_{if}$ are probability amplitudes? This right here that this on top of each diagram, Why is it you cancel my questions that I asked anything special this is not cool I just wanted a help and ...
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Is the contribution of diagrams without vertices taken into account in calculating the process amplitude?

It seems I have finally decided on the question. When expanding the interaction process in a perturbation theory series, it is also necessary to take into account the contribution of the diagrams in ...
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How to distinguish first-order Feynman diagrams from the rest? [duplicate]

On what basis is it determined to what order the given Feynman diagram belongs? Does it depend on the number of interaction vertices? For example, two vertices are first order, four vertices are ...
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Third-order Feynman diagrams of 2-point function in $\phi^4$-theory [closed]

$\newcommand{\Braket}[1]{\left<\Omega|#1|\Omega\right>}$ Hello, I am currently studying QFT and have a problem concerning the 2-point correlation function in $\phi^4$-theory. When I draw all the ...
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Example of truncated expectation which gives a disconnected diagram. Where am I wrong?

My notes introduce the truncated expectation in the following way: given $S_0$ a quadratic form, consider a generating function $$e^{W(J)} = \int \prod_x d\varphi_x e^{-S_0+ JO} = \int P(d\varphi) e^{...
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Cancellation of vacuum bubbles in the correlation function

$$ G_K = \langle\Omega|T\prod_{i=1}^{2K}\phi(x_i)|\Omega\rangle. $$ A problem sheet question asks you to 'Show that the contribution to $G_K$ of $O(λ_L)$, $L$ integer, in which all external points are ...
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Symmetry factors for feynman diagrams from complex scalar interaction term

My question regards a quantum field theory with an interaction term $${\mathcal{L_{int}}=-\frac{\lambda}{4}\phi^\dagger}^2 \phi^2.$$ It's claimed in the solutions to a problem sheet that the one-loop ...
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How are the usual measurement in quantum mechanics related to the description of interaction by Feynman diagrams?

Try to formulate the question more clearly. Using Feynman diagrams, the amplitude of particle interaction is calculated, and through it, the probability of detecting this interaction in an experiment. ...
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Symmetry factor of Feynman diagram in $\phi^4$ theory at second order

I am trying to figure out the symmetry factor of the above diagram in the $\phi^4$ theory. The correct answer is $S=4$ (in that the Feynman diagram gets a multiplicative factor of $\frac{1}{4}$) but I ...
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Summing of neutrino spins in Muon decay

This might be a silly question, but I am just a beginner so please bear with me. When we average the matrix element over spins, do we also have to sum over neutrino spins since neutrinos are only Left-...
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How to calculate the process correctly using Feynman diagrams?

The general approach of perturbation theory is familiar to me, only a slight clarification. We describe the interaction of two particles. For this, one must first take into account the contribution of ...
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133 views

What happens in the interval between the initial and final states of the interaction process?

Let's say there is a process of scattering of a photon by an electron. The process has a certain amplitude, the square of the modulus of which determines the probability that the measurement will ...
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What are extrinsic and intrinsic flavour production?

In terms of Feynman diagrams, what are extrinsic and intrinsic flavour production? See for example this paper this paper (p.2).
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What is the generalization of the path integral to the case of particle interaction?

I can hardly remember, so please correct if I am mistaken. In path integral formulation, the probability of detecting a quantum particle at a given point in space is calculated through the integral of ...
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Symmetry factor for Feynman diagram in scalar field theory [duplicate]

I am trying to calculate the symmetry factor for a particular Feynman diagram (the one in the picture attached). Using a method that has worked for me every time, I get 1/4, but according to homework ...
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Is there a $t$-channel process for $q\bar{q} \rightarrow gg$? [duplicate]

Let's consider the process $q\bar{q}\rightarrow gg$. Is the following Feynman diagram allowed: I ask because of the following reason: At the upper vertex, the $q$ emits a gluon $g$ and the propagator ...
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How to apply Feynman rules of counterterms to calculate amplitudes?

Consider $\phi^4$-theory with counter-terms and renormalized mass, field and coupling constant, described by the Lagrangian $$\mathcal{L}= \underbrace{\frac{1}{2} \partial_{\mu} \phi_{r} \partial^{\mu}...
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How to construct 4 external lines Feynman diagram from 3 external lines Feynman diagram?

From Renormalization talk/idea by Sean Carroll, when he talks about effective field theory: but then I could construct from that the following diagram with four lines in it In previous talks he ...
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What is the Mediator in this Feynman Diagram $q\bar{q} \rightarrow gg$?

Let's consider the t-channel version of the process $q\bar{q} \rightarrow gg$. What is the mediator in this case, a $q$ or a $\bar{q}$? Naively, I would have thought a $q$ (as to have one fermion line)...
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How Would a Feynman Diagram Look Like for a Proton-Proton Collision?

The LHC is a proton-proton collider. If I wanted to draw a leading order Feynman diagram for a two-quark production in proton-proton collisions, would it be correct to draw sth like this, or would ...
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Can particles running in a loop go on-shell and does this create a “resonant” effect?

Are there any Loop diagrams, where we need to consider the internal propagator with a additional $i\Gamma m$ in the denominator to get a finite result (apart from adding counterterms). If yes does ...
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Process of interaction of two particles from the point of view of quantum mechanics

I have not opened the textbook for a long time and may have forgotten something, but, as far as I remember, to describe the interaction of two particles it is necessary to integrate this process ...
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What happens to an electron when it radiates a photon?

I recently came across this Feynman diagram: For a more simplistic diagram, I suppose even this would be adequate: As you can see in these diagrams, they radiate these virtual photons. The virtual ...
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On which propagator does the field self-contraction loop go on this Feynman diagram?

This question relates to page 111 in Peskin and Schroeder. I am trying to do the derivation of the 2-particle to 2-particle Feynman diagrams in $\phi^4$ theory by hand, following Peskin and Schroeder. ...
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Computing symmetry/combinatorial factor for a diagram in $\phi^4$ theory

I am working with $\lambda\phi^4/4!$ theory and am struggling to compute the symmetry factor for the diagram by using the method specified here. I know that the answer is ${1}/{12}$, but I can't work ...
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Do sum rules for spectral function always hold?

In condensed matter physics, we can define the spectral function as $$ A_{\alpha}(\omega) = -\frac{1}{\pi}\mathrm{Im}G_{\alpha}^R (\omega) $$ It can be shown that this quantity satisfies the sum rule: ...

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