What is Feynman diagrams: Definition and 150 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. Xico Sim

    I Elementary processes in Feynman Diagrams

    Hello there. I'm attending an introductory course in particle physics. We're supposed to know how to draw first-order tree level Feynman diagrams for simple reactions. I've been struggling to understand the method I should follow in order to correctly draw them. As I understand it now, we can...
  2. A. Neumaier

    Insights Misconceptions about Virtual Particles - Comments

    A. Neumaier submitted a new PF Insights post Misconceptions about Virtual Particles Continue reading the Original PF Insights Post.
  3. C

    I Feynman diagrams and the Wick contraction

    Consider a real scalar field described through the following lagrangian $$\mathcal L = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi - \frac{1}{2}m^2 \phi^2 - \frac{g}{3!}\phi^3$$ The second order term in the S matrix expansion produces the diagrams in which we have a ##2 \rightarrow 2##...
  4. F

    I Virtual particles in Feynman diagrams and not

    I know some people here hate the subject of virtual particles. So I will try to narrow my questions. Granted, virtual particles are just attempts to describe the math and are not real in and of themselves. But there seem to be a couple of different kinds of virtual particles (in the math)...
  5. Glacier Studio

    Comprehensive Particle Scattering Table

    For particle physics research reference and education purposes, it's often convenient to have comprehensive particle scattering tables and Feynman diagrams at hand for analysis. May I ask whether there is a web site, app, or ebook that dynamically generates comprehensive scattering tables for...
  6. P

    Feynman diagram; ##\pi^0+\pi^0\rightarrow \pi^++\pi^-##

    Homework Statement For the reaction below draw three Feynman diagrams, one that proceeds through exchange of a gluon, one through a photon and one exchanging a weak W-Boson. ##\pi^0+\pi^0\rightarrow \pi^++\pi^-## Which diagram provides the dominant contribution for this reaction? Explain how...
  7. FrancescoS

    Dyson equation and Feynman diagrams: a brief explain

    Hi! I have found a note about Generating functionals that seems to be very direct. Since I faced a difficulty many times without solve it, I would like if anyone can explain me my troubles. You can fine the note here (link). In the following figure, the author describes the 3-point green...
  8. Immortalis

    Learning Feynman Diagrams: Matrices & Dirac Adjoints

    I am trying to learn about Feynman diagrams and am confused by some of the notation. In particular, what do matrices, in particular the Dirac adjoint, have to do with Feynman propogators and why are they in imaginary terms?
  9. H

    Using Feynman rules to calculate amplitude

    Given a diagram, how is one supposed to apply the feynman rules to calculate the feynman amplitude?
  10. H

    How to calculate Feynman diagrams in phi^4

    For quartic scalar field theory these are some of the lowest order diagrams (taken from the solutions to 9.2 srednicki). I'm wondering if someone can give me an intuition of how to actually calculate them. What I'm thinking is that vertices are $$\int \frac{d^{4}x}{(2\pi)^{4}}$$ and for the...
  11. H

    Order of scalar interaction impact Feynman diagrams

    On page 60 of srednicki (72 for online version) for the $$\phi^{3}$$ interaction for scalar fields he defines $$Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta J})^{3}\right]Z_0(J)$$ Where does this come from? I.e for the quartic interaction does this...
  12. T

    ELI5: Antiparticles in Feynman Diagrams

    Hi!, I am studying for an introductory course in QED and Feynman Diagrams. Everything we see is like a first order approach and I am having some trouble understanding antiparticles in Feynman Diagrams: Why is it that we put an antiparticle that is leaving as if it is entering the interaction...
  13. Andrea M.

    Drawing Feynman diagrams with feynarts

    I'm trying to draw Feynman diagrams with the feynarts.sty package for LaTex. The problem is that if I write the following code \begin{feynartspicture}(150,150)(1,1) \FADiagram{} \FAProp(0.,10.)(6.,10.)(0.,){/Straight}{0} \FALabel(3.,9.18)[t]{$1$}...
  14. S

    Feynman diagrams for phi phi -> phi phi

    Homework Statement Compute the matrix element for the scattering process \phi \phi \to \phi \phi Homework Equations The Lagrangian is given by L = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi + \frac{\alpha}{2} \phi \partial_{\mu} \phi \partial^{\mu} \phi + \frac{\beta}{2} \phi^2...
  15. M

    What Are the Feynman Rules for Bremsstrahlung with Vector Particle Production?

    So this isn't a homework problem really, but based on the posting rules for the HEP section this seems to fit better here. My issue is that I'm trying to use a Feynman diagram to represent a Bremsstrahlung process in which a vector particle is produced: $$ Z + e^- \rightarrow Z + e^- + v. $$...
  16. G

    Lagrangian of fields from Feynman diagrams

    ¿How is possible deduce the Lagrangian of the fields of a theory knowing only his Feynman Diagrams?
  17. C

    How to draw Feynman diagrams

    I am reading the book tilted "quantum field theory in a nutshell(second version)" by A.Zee. On the page 45, for example there is a term \frac{1}{m^2}λJ^4. The question is that how to related it to the Figure 1.7.1. or that, How can I draw the three diagrams in Figure 1.7.1 from the term...
  18. Safinaz

    Understanding Color Factors in Feynman Diagrams

    Hi there, In paper as : http://authors.library.caltech.edu/8947/1/GREprd07.pdf I don't understand the colour factor associated with two gluons and single octet scalar as the first Feynman diagram in fig. 3 ? In eq. 27, this colour factor is given by ## (d^{abc})^2 ## .. so, how did this come...
  19. rolotomassi

    Green's Functions and Feynman Diagrams

    I've been learning about Greens functions. I'm familiar with how to find them for different differential operators and situations but far from fully understanding them. We were shown in lecture how they can be used to obtain a perturbation series, leading to Feynman diagrams which represent...
  20. CAH

    Feynman Diagrams, exchange particle?

    Exchange Particles are to show the transfer of (for example) +/- charge to the other side so the charges balance. But I don't understand... Beta plus decay: p → n + e+ + νe. This is just an example, the Feynman diagram shows a W+ boson transferring the positive charge to the right hand side...
  21. U

    What Are Feynman Diagrams and How Are They Used in Physics?

    Homework Statement (a) e- + e+ -> e- + e+ (b) e- + e- -> e- + e- c) e- + e- -> e- + e- + u+ + u- d) y -> e+ + e- e) y + y -> y + y Homework EquationsThe Attempt at a Solution Part (a)[/B] Part (b) Part (c) Part (d) Part (e) Not sure what to do with this, since usually the...
  22. D

    Momentum conservation at vertex in Feynman Diagrams

    Hey guys, I need help with conserving momentum at these vertices (this is Bhabha scattering): So in Diagram (a), the first vertext to the left. The incoming momenta are p_{1}+p_{2}. The outgoing momentum I'll call it p. So...shouldnt I have p_{1}+p_{2}=p? Furthermore, is the propagator...
  23. M

    How many Feynman diagrams do I draw?

    I'm currently going through the interaction part of Tong's lecture notes on quantum field theory, and I'm a bit confused about how many Feynman diagrams I need to draw in order to compute the amplitude of various interaction terms. Tong presents Feynman diagrams through a series of examples. For...
  24. ChrisVer

    LaTeX LaTeX question about Feynman Diagrams

    Has anyone of you tried to work with creating Feynman Graphs in LaTeX? I tried using the feynmf package, as explained here: https://www.sharelatex.com/learn/Feynman_diagrams and used the same introductory script: \begin{fmffile*}{diagram} \begin{fmfgraph}(40,25) \fmfleft{i1,i2} \fmfright{o1,o2}...
  25. Breo

    Order of the symmetry group of Feynman Diagrams

    Hello, I am learning Feynman diagrams and I still do not understad quite well the symmetry factor idea. The equation is: $$ \frac{1}{O(G)} = \frac{M}{n!(4!)^n} $$ I was trying the next example: If I am not wrong it is O(G) = 10 taking care of the asymmetry of each pair of internal lines...
  26. Breo

    Feynman Diagrams: Polarization question

    Hello folks, I've just started to read "An Introduction to Quantum Field Theory by Peskin and Schroeder" and at the end of 6th page I could read: "... Since H_I should conserve angular momentum, the photon to which these particles couple must have the correct polarization vector to give it...
  27. T

    Identical particles and Feynman diagrams

    In Introduction to QFT (peskin) 4.5, he writes: The computation for M, of course, will be quite different when identical particles are present. However, I have finished reading the first part of the book and found no special treatment for identical particles. Can anybody tell me how to...
  28. R

    Feynman Diagrams homework help

    Homework Statement For the following reactions draw Feynman diagrams, clearly labelling all the quarks, leptons and exchanged particles and stating the type of interaction involved (if more than one interaction could be involved give the most likely): (i) ##\pi^0 \to \gamma + \gamma##...
  29. Greg Bernhardt

    What is the Role and Significance of Feynman Diagrams in Quantum Physics?

    Definition/Summary Feynman diagrams are a combinatorial device for enumerating a sum of integrals of products of delta functions. Feynman diagrams are a mathematical tool with no physical significance. In particular, no single Feynman diagram is intended to represent any physical...
  30. M

    On tree level Feynman diagrams

    Hi folks, I'm assured that scattering cross-sections in QFT computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring in QED corresponds to scattering of classical point charges. But I'm not sure I...
  31. Spinnor

    Feynman diagrams with odd number of vertices.

    If we scatter unpolarized electrons off each other and we calculate the amplitude for electrons to scatter into final states and one photon to be emitted do we get destructive interference because the photon can be emitted by either electron? Is one photon emission suppressed in favor of an even...
  32. S

    A question about Feynman diagrams

    For a 2nd order electron-positron scattering, the following diagrams are possible: http://www.quantumdiaries.org/wp-content/uploads/2010/02/eepp-1024x228.png My question is: What is the meaning of the right diagram - is a photon created and annihilated instantaneously? how is this possible?
  33. D

    Drawing a Feynman Diagram: Lagrangian Basics

    I need help :( How can I draw a Feynman Diagram, starting with a Lagrangian?
  34. S

    Showing Beta Decay (Feynman diagrams?)

    Would someone please tell me how I would show Strontium-90 decay into Yttrium 90(and emitting Beta particles)? Would I need to use a Feynman diagram? Thank you!
  35. C

    Question about Feynman diagrams with the integral

    I read the book of "quantum field theory in nutshell" by A. Zee. There is a "baby problem" in Page 44. I can't understand how to get the diagrams of Figure 1.7.1 from the calculation of -(\lambda/4!)(d/dJ)^4 differentiating [1/4!(2m^2)^4]J^8. How to associate this term to the three diagrams...
  36. Thor Shen

    From Feynman diagrams to potential

    I met a problem when I read the textbook "Relativistic Quantum Mechanics" by J.D.Bjorken. He said we can get the potential V(r_1,r_2)=\frac{f^{2}}{\mu^{2}}(1-P_{ex})(\tau_1\cdot\tau_2)(\sigma_1\cdot\nabla_1)(\sigma_2\cdot\nabla_1)\frac{e^{-\mu|r_1-r_{2}|}}{|r_1-r_{2}|} (10.51) from the...
  37. J

    Feynman diagrams and momentum conservation

    I understand that Feynman diagrams can be expressed either in the position or momentum representation. Is the 4-momentum conserved at the vertices in each case or only in the momentum representation?
  38. M

    What is the Feynman diagram for Higgs decay to Z and gamma particles?

    Hi, I am drawing Feynman diagrams for various Higgs decay channels. There are two diagrams I am stuck on and there aren't many examples online. They are H→gg and H→Z\gamma For the H→gg decay I had a stab at drawing the reverse of the gluon fusion diagram. Higgs decaying to two gluons via a...
  39. H

    Elementary question on Moller Scattering Feynman diagrams

    Greetings, I think this will be a very quick thread. I am new to using Feynman diagrams, and have run into something that I find puzzling. The lowest-order Coulomb interaction Feynman diagram is (image from Wikipedia Moller Scattering article)...
  40. P

    Calculating & Drawing Feynman Diagrams for $\mathscr{L}$

    Homework Statement I need to calculate <\phi(x_1)\phi(x_2)\phi(x_3)> and <\phi(x_1)\phi(x_2)\phi(x_3)>_{c} and then draw Feynman diagrams when \mathscr{L} = -\left(\left(\partial_{\mu}\phi\right)^{2} + m^{2}\phi^{2}\right) - g\phi^{3} through first order in g. Homework Equations...
  41. tom.stoer

    List of matrix elements or Feynman diagrams

    Is there a list of matrix elements for elementary processes? ##f\bar{f}\to\gamma\to f^\prime\bar{f}^\prime## ##f\bar{f}\to Z^0\to f^\prime\bar{f}^\prime## ##ff^\prime\to W \to \ldots## ##qq^\prime\to \ldots## ##\ldots##
  42. omephy

    What are the disconnected Feynman diagrams in QFT?

    I am learning QFT from Srednicki's book. However, in Figure 9.2 Srednicki has given all connected diagrams with E=0 and V=4. Are there any way to know the disconnected diagrams? Can you tell me what they are.
  43. C

    Feynman diagrams - electrical charges

    I have a request for some explanation in Feynman diagram concerning repelling/attraction of electrical charges. I have been told that when two charges (say, e1(-) and the e2(-)) repel each other, a photon is being emitted from one of them, and the other charge is later being hit by this photon...
  44. D

    Understanding Neutral Pions: Superpositions, Particles, & Feynman Diagrams

    So apparently a neutral pion is a superposition of u\bar{u} and d\bar{d}. I'm having trouble understanding what this means. I have no problem understanding how the decay products of some scattering experiment could be a superposition of these two states, but how can we treat this superposition...
  45. Demon117

    Significance of Order in Feynman Diagrams

    I've been doing some review of particle physics in Griffiths and I came across this statement that really didn't stand out to me before. "the idea is to draw all the diagrams contributing to the process in question (up to a desired order), calculate the amplitude (M) for each one, and add...
  46. M

    Characteristics of Feynman diagrams for correlators at a given order of lambda

    I've been given an action of S = -\frac{1}{2}m^2\phi^2 - \frac{\lambda}{3!}\phi^3 and the question then require drawing the feynman diagrams for the <\phi\phi> at order \lambda^2. I am told that there are 2 connected diagrams at one-loop order and one disconnected two-loop diagram and...
  47. N

    Understanding Quark-Gluon Interactions: Deciphering Feynman Diagrams

    Hi all. I am new here but i decided to work a bit more and finish my diploma faster so i think i will use this forum more from now on. I was studing about quark color changes, quark interactions, gluons and generally the strong force. As i saw the Feynman diagrams i felt a bit confused...
  48. MalachiK

    What is the correct convention for anti-fermions in Feynman diagrams?

    Hi Guys. I'm hoping that you might be able to help me out with a question I have about anti-particles in Feynman diagrams. I'm drawing these again for the first time in over a decade because I'm teaching an elementary physics course that requires the students to draw diagrams for a few...
  49. Spinnor

    Feynman diagrams from Quarks and Leptons Halzen and Martin?

    Feynman diagrams from "Quarks and Leptons" Halzen and Martin? The following scan is from Quarks and Leptons: An Introductory Course in Modern Particle Physics, Francis Halzen (Author), Alan D. Martin (Author), page 9. Can I take anything from the topological difference between figure (b) and...
  50. G

    Changing the sign of 4-momenta in Feynman diagrams

    If a Feynman diagram only involves bosons, then can you multiply all external 4-momenta by negative one, and still get the same amplitude? Looking at the Feynman rules this seems true. If the diagram has a fermion (as real or virtual particle), then it seems this is no longer true. I just...
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