What is Feynman diagram: Definition and 167 Discussions

In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations which won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagrams, as would [Wilczek's] calculations that established a route to production and observation of the Higgs particle."Feynman used Ernst Stueckelberg's interpretation of the positron as if it were an electron moving backward in time. Thus, antiparticles are represented as moving backward along the time axis in Feynman diagrams.
The calculation of probability amplitudes in theoretical particle physics requires the use of rather large and complicated integrals over a large number of variables. Feynman diagrams can represent these integrals graphically.
A Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory. Within the canonical formulation of quantum field theory, a Feynman diagram represents a term in the Wick's expansion of the perturbative S-matrix. Alternatively, the path integral formulation of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to the final state, in terms of either particles or fields. The transition amplitude is then given as the matrix element of the S-matrix between the initial and the final states of the quantum system.

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  1. Alpha2021

    A How to calculate Feynman amplitude in Fish diagram

    I am familiar with the process of calculating cross sections using tree-level Feynman diagrams. Currently, I'm keen on learning how to calculate the Feynman amplitude for a specific diagram displayed in the attached images. I'm wondering if there are any study materials available that offer a...
  2. N

    Feynman diagram for ##\mu^+\mu^-## production in ##p\bar{p}## reaction

    I was able to solve b) but I am confused for a). I understand that in the proton-antiproton collision, only two quarks (one from proton and other from anti-proton) can be combined to get a virtual photon that in turn creates muon and anti-muon. I don't understand what would happen to the other...
  3. James1238765

    I What is the probability of an electron emitting a photon?

    I have seen many tutorials that provide steps how to transcribe a Feynman diagram into algebra, for instance [here]: However, I have never seen the final line of the calculation converted into a real number. What are the steps to get from the algebra equations transcribed using the Feynman...
  4. P

    Which Feynman diagram or diagrams include feasible processes?

    Hello friends. I couldn't do it. Which Feynman diagram or diagrams has include feasible process?
  5. N

    Is my Feynman diagram for production of ##W^-## boson correct?

    I think ##X## appears to be ##\pi^{+}## because it is light and energetically more favourable. Pion should be positive to ensure charge conservation. I am stuck at drawing a Feynman diagram for $$p+\bar{p} \to W^- + \pi^+$$. Is this correct? Is this the leading order diagram or is there a...
  6. G

    I Exploring the Feynman Diagram of γ+γ→γ+γ: What Does It Reveal?

    If you have γ+γ→γ+γ what would the Feynman diagram look like (time-ordering implied). I think it will be a square with four photons on each vertex but is this all there is to it or am I missing something?
  7. U

    Calculating Amplitude in Standard Model

    Hi! I'd like to ask you if my calculation of the amplitude on the mentioned process in the Standard Model is correct. The three diagrams contributing at lowest order should be where in the middle one the two Higgs boson are NOT forming a quartic interaction vertex. My attempt at calculating the...
  8. W

    A Measurement from Feynman diagram

    hi, can anyone please give me the list of measurement we can do ON Feynman diagram? Like , branching ratio, cross-section etc
  9. J

    A Feynman diagram for bound particle output

    I am interested on how Feynman diagram is formed from a differential equation model of particle interaction wherein the incoming particles are not bound (e.g., separated neutron, proton and electron) and one or more of the outgoing particles are bound (e.g., hydrogen atom). However, I had never...
  10. G

    I Feynman diagram for scalar - vector interaction

    The term for the electromagnetic interaction of a Fermion is ##g \bar{\Psi} \gamma_\mu \Psi A^\mu##, where ##g## is a dimensionless coupling constant, ##\Psi## is the wave function of the Fermion, ##\gamma## are the gamma matrices and ##A## is the electromagnetic field. One can quite simply see...
  11. snypehype46

    Amplitude of Feynman diagram in ##\phi^4## interactions

    This is not really homework assigned to me but I wasn't sure where to post this. I'm trying to work through the book "Quantum Field Theory for Gifted Amateurs" by Tom Lancaster. I'm doing the questions on Chapter 19 to understand how to draw Feynman diagrams and work out their amplitude. One of...
  12. JD_PM

    Loop Feynman diagram contributions to correlation functions

    My understanding of the n-correlation function is \begin{equation*} \langle \phi(x_1) \phi(x_2) ... \phi(x_n)\rangle = i \Delta_F (x_1-x_2-...-x_n) \end{equation*} Where ##\Delta_F## is known as the Feynman propagator (in Mathematics is better known as Green's function). Let us analyze...
  13. M

    Showing that this identity involving the Gamma function is true

    My attempt at this: From the general result $$\int \frac{d^Dl}{(2\pi)^D} \frac{1}{(l^2+m^2)^n} = \frac{im^{D-2n}}{(4\pi)^{D/2}} \frac{\Gamma(n-D/2)}{\Gamma(n)},$$ we get by setting ##D=4##, ##n=1##, ##m^2=-\sigma^2## $$-\frac{\lambda^4}{M^4}U_S \int\frac{d^4k}{(2\pi)^4} \frac{1}{k^2-\sigma^2} =...
  14. M

    How to translate expression into momentum-space correctly

    This seems rather straight forward, but I can't figure out the details... Generally speaking and ignoring prefactors, the Fourier transformation of a (nicely behaved) function ##f## is given by $$f(x)= \int_{\mathbb{R}^{d+1}} d^{d+1}p\, \hat{f}(p) e^{ip\cdot x} \quad\Longleftrightarrow \quad...
  15. Martian2020

    B How to construct 4 in+out Feynman diagram from 3 Feynman diagram?

    Renormalization talk by Sean Carroll, "but then I could construct from that the following diagram with four lines in it": In previous talks he explained about diagrams and told interaction can be represented by many (even infinite) number of diagrams, "in" line can be changed to antiparticle...
  16. steve1763

    A Exploring Free and Interaction Terms of L in Quantum Field Theory

    With free part L=-½(∂Φ)^2 -½m^2 Φ^2 and interaction term L=½gΦ^2Any help would be appreciated, thank you.
  17. ShayanJ

    A Developing the Feynman diagram expansion

    I'm reading "introduction to many body physics" by Piers Coleman. In section 7.2 he's trying to introduce Feynman diagrams by expanding the generating functional. But first he transforms it into this pictorial form: Then he calculates the n=1, m=1 term like below: Which I understand. But I...
  18. tomdodd4598

    I QED - ordering of Feynman diagram rules

    Hey there, In QED, we often have Feynman diagrams involving various numbers of non-commuting components, such as for the one-loop vertex correction (Peskin & Schroeder, page 189): The diagram this integral corresponds to is: How do we choose which order to put the propagators and vertex...
  19. saadhusayn

    A Two loop Feynman diagram with quartic vertex

    I am trying to calculate the effective potential of two D0 branes scattering in Matrix theory and verify the coefficients in this paper: K. Becker and M. Becker, "A two-loop test of M(atrix) theory", Nucl. Phys. B 506 (1997) 48-60, arXiv:hep-th/9705091. The fields are expanded about a constant...
  20. M

    I How to determine Spinor in Feynman diagram

    Consider Moller scattering, that is $$e^-(\vec p_1, \alpha)+e^-(\vec p_2, \beta) \quad\longrightarrow\quad e^-(\vec q_1, \gamma)+e^-(\vec q_2, \delta),$$ where the ##\vec{p}_i,\vec q_i## label the momenta of the in and outgoing electrons and the greek letter the spin state. The two relevant...
  21. ronnie snooker

    B Does the Feynman diagram process actually exist, or is it just for computation?

    i want to known whether virtual particle exist or not , and does exchange of particle really happen in interaction.
  22. Physicsphysics

    Pion annihilation Feynman diagram

    π+ + π- → γ + γ How do you represent this in a Feynman diagram showing the individual quark? I am very confused please help! [Moderator's note: Moved from a technical forum and thus no template. Own effort below.]
  23. G

    Feynman diagram with TikZ-Feynman

    Hi, I'm learning how to draw Feynman diagrams in LaTeX using the TikZ-Feynman package, but in https://arxiv.org/ftp/arxiv/papers/1601/1601.05437.pdf I don't see if it's possible to draw loops in ##\lambda \phi^4## theory, how can I draw a loop that goes from one vertex to itself? Thanks
  24. takunitoche

    Three gauge boson Yang-Mills vertex

    Hello everyone, I am stuck in deriving the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is $$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$ I have rewritten this term using the...
  25. Michael Price

    A Massive gauge bosons in QFT in/out states

    Because massive gauge bosons have a finite half life, are they excluded from the (infinitely, asymptotically remote?) in and out states of QFT? Or, to put it another way, are they restricted to the internal legs of Feynman diagrams, i.e. to being virtual only? We can see W and Z tracks in...
  26. R

    I Young physicist in seek of guidance

    Is there anyone on here who could help me fill in my gaps in quantum field theory up to renormalization? I know how to canonically quantize a theory and how to use scalars (spin 0), vectors (spin 1) and spinors (spin 1/2) but lack more advanced knowledge like renormalization which I could...
  27. nomadreid

    I Compton scattering in a Feynman diagram

    Attempting to understand the following: Compton scattering can happen either (a) an electron could absorb a photon and later emit a photon, or (b) an electron could emit a photon and later absorb a photon. OK, the maths works out, but I am trying to get intuition on track. These two are...
  28. Raymont

    Divergence of the amplitude for a Feynman diagram

    1. The problem statement In calculating the amplitude for the diagram[1], view 1.jpg. [1] Voja Radovanovic, Problem Book Quantum Field Theory 2. Homework Equations View 2.jpg. The Attempt at a Solution View 3.jpg.[/B] Why the integrals is divergent? Why the other terms are finite?
  29. Cardinalmont

    B Feynman Diagrams: Uncovering the Issue

    Hello, I assigned a work packet to my IB Physics students that guides them through how to make Feynman diagrams. This particular problem seems to have some issue, but perhaps it is something that myself and my class have all over looked. Note: At the beginning of the packet it states that some...
  30. H

    A Two questions on Feynman diagram and Green's function

    First, is it suitable to solve a Green's function by one-order self-energy, since it only consider partial high order perturbation, so it's unclear that this calculation corresponding to which order perturbation. In other word, if one wants to use self-energy to get Green's function, he should...
  31. Glenn Rowe

    A Scalar-scalar scattering Feynman diagram

    I'm trying to work out the Feynman diagrams for scalar-scalar scattering using the Yukawa interaction, as given in Chapter 6 of Lahiri & Pal's A First Book of Quantum Field Theory. The interaction hamiltonian is $$\mathscr{H}_{I}=h:\overline{\psi}\psi\phi:$$ where ##\psi## is a fermion field and...
  32. C

    Solving for X's Baryon & Lepton Number

    Homework Statement Homework EquationsThe Attempt at a Solution I worked out that the baryon number of X is 0 and the lepton number is +1 which means x is a lepton. However, when I work out the charge of X, do I add W+ to the left hand side or right hand side of the equation? [/B]
  33. M

    Feynman Diagrams for Interacting Scalar Fields

    Homework Statement Consider four real massive scalar fields, \phi_1,\phi_2,\phi_3, and \phi_4, with masses M_1,M_2,M_3,M_4. Let these fields be coupled by the interaction lagrangian \mathcal{L}_{int}=\frac{-M_3}{2}\phi_1\phi_{3}^{2}-\frac{M_4}{2}\phi_2\phi_{4}^{2}. Find the scattering amplitude...
  34. P

    I Virtual particles in Feynman diagrams

    In the first diagram above, if I understand it correctly, the photon turns into an electron positron pair and then back again to a photon. However, what exactly is happening in the second diagram at the bottom left hand corner? Is the electron being converted to an electron photon pair?
  35. P

    I Calculating the fine structure constant in Feynman diagrams

    Griffith's Introduction to Elementary Particles, if I understand it correctly, states that in QED, the fine structure constant contributes less and less to the strength of the EM interaction as we add more and more vertices since the constant is so small (1/137). However, in QCD, since the...
  36. P

    I Why is there an arrow mediating a process in a Feynman diagram?

    In the following Møller scattering process, two electrons enter, exchange a photon and then leave (and if I understand this correctly, we say that both of the electrons emitted a photon). However, in this case: We have an electron scattering off a photon, but the interaction happens by an...
  37. heavybuilder

    I A question about a Feynman Diagram

    Could somebody explain me this?: Why is the arrow of the electron-antineutrino pointed towards the W-boson and not as in the second picture upwards? This is my first post and also haven't learned too much about physics yet so please if anything is unclear hit me up.
  38. D

    I Understanding Neutron Star Formation Through Feynman Diagrams

    Hello, I recently watched a video as an introduction to Feynman diagrams for my own self-interest. The video gave a link to practice problems, and one of them was as follows: In a neutron star gravitational collapse causes valence electrons to combine with protons. Draw a Feynman diagram...
  39. S

    I Feynman Diagram for Double Charm Baryon

    This Feynman diagram accompanied the announcement on the public LHCb site. How would you describe the origins of the up and down quark anti-quark pairs that that contribute to the decay of the ##\Xi_{cc}^{++}##?
  40. L

    I Feynman diagram of the Vector Boson Fusion

    Hi, I would like to ask you how to properly describe the Feynman diagram of the Vector Boson Fusion where the Higgs boson is produced. Two quarks scatters two vector bosons (that means boson W or Z) at some moment which influence each other and produce the Higgs boson. Is that right...
  41. S

    I Matrix Elements via Feynman Diagrams

    Hello everyone, I am currently trying to understand how we can use feynman diagrams to estimate the matrix element of a process to be used in fermi's golden rule so that we can estimate decay rates. I am trying to learn by going through solved examples, but I am struggling to follow the logic...
  42. Safinaz

    I Dominant Feynman diagram for ##b \to s ~l^+ l^−##

    Hi all, It's written in QFT books, see for instance George_W._S. book "Flavor Physics and the TeV Scale" that the following Feynman diagram (1) is the dominant Feynman diagram for ## b \to s ~l^+l^− ## decay. Actually I compare this diagram via another possible diagram (2) Both (1) and...
  43. C

    I Identifying gluon in Feynman diagram

    Consider the process in the picture below where an ##r \bar r## state goes to an ##r \bar r## state through mediation of a gluon. The gluon may carry the colour anticolour combination ##r \bar r##. I'm just wondering... 1) Can we have a gluon with the colour assignments just ##r \bar r##? If...
  44. CassiopeiaA

    I Exchange of photons inside atoms

    I was reading Feynman Diagrams and stumbled upon this query: If the electrons and protons interact by exchange of photons, does the electron inside an atoms also interact with the nucleus with a similar kind of exchange?
  45. 1

    I I don't understand this Feynman Diagram

    Question: Draw the lowest-order Feynman diagrams for the e+e- --> W+W-process The answer gives three diagrams. I understand the first two, but the third makes no sense to me. Here it is: So this is a t-channel Feynman diagram. As far as I can tell regarding how these types of Feynman diagrams...
  46. Safinaz

    I How to Calculate the Self Energy Amplitude of a Sunset Diagram?

    Hi all, I'd like to calculate the self energy amplitude of the following sunset diagram (take the middle for instance ) can anyone help me in distributing the momentum on the internal propagators ? Best
  47. Safinaz

    I How to calculate self energy Feynman diagram like that

    Hi all , I try to calculate the squared amplitude of the following self energy digram : where se is massless Dirac fermion , and vrm is massless right handed neutrino. x is a scalar with mass m .. I wrote the nominator of this process as: N = ## \bar{u}(p) (1-\gamma_5) (p\!\!\!/ +k\!\!\!/ )...
  48. ShayanJ

    A Vertex, Propagator and Loop counting

    I'm reading these lecture notes but there is something I don't understand. In page 15, it starts to consider vacuum diagrams of various orders and tries to associated a factor to them according to the rule: ## diagram \sim (\frac \lambda N)^p(\frac N \lambda)^v N^l=\lambda^{p-v} N^{l+v-p}##...