What is Feynman diagrams: Definition and 147 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. Ramtin123

    A Renormalisation of the Fermionic triangle loop

    I am trying to renormalise the following loop diagram in the Standard Model: Using the Feynman rules, we can write the amplitude as follows: $$ \Gamma_f \sim - tr \int \frac{i}{\displaystyle{\not}\ell -m_f} \frac{i^2}{(\displaystyle{\not}\ell+ \displaystyle{\not}k -m_f)^2} \frac{d^4 \ell}{(2...
  2. A

    I How does electric attraction work at subatomic scales?

    In Feynman diagrams, I believe two like-charged particles will "blast" one another with a photon, thus pushing each other away because of the law of conservation of momentum. How would this work for electric attraction?
  3. P

    I Confusion about Scattering in Quantum Electrodynamics

    When it comes to scattering in QED it seems only scattering cross sections and decay rates are calculated. Why is that does anyone calculate the actual evolution of the field states or operators themselves like how the particles and fields evolve throughout a scattering process not just...
  4. H

    I Feynman diagrams and sum over paths

    Hi ! In a Feynman diagram, can we consider that the propagator specifying the transition amplitude of a particle (let's say, of a "real" electron, or of a "virtual" photon) between two points or two vertices, is in fact itself the sum of a multiplicity of probability amplitudes, each one...
  5. PhysicsRock

    LaTeX LaTeX formatting Feynman Diagrams incorrectly

    I've been trying to get Feynman Diagrams to work in my LaTeX code, however, the output is not what it is supposed to be. I'm using TeXMaker and TikZ-Feynman to draw the diagrams. My code looks like this: \feynmandiagram [horizontal=a to b] { i1 -- [fermion] a -- [fermion] i2, a -- [photon] b...
  6. dextercioby

    A First order electroweak correction to the g-2 magnetic moment

    We know that we need to go to 5th order in perturbation theory to match 10 decimals of g-2 for electron, theory vs. experiment. But let us not assume QED is pure and independent, but it's a lower energy limit of GSW (not Green-Schwartz-Witten from superstrings) electroweak theory. Has anyone...
  7. M

    Feynman rules and the tree level cross section of two scalar fields

    Hi there. I'm trying to solve the problem mentioned above, the thing is I'm truly lost and I don't know how to start solving this problem. Sorry if I don't have a concrete attempt at a solution. How do I derive the Feynman rules for this Lagrangian? What I think happens is that in momentum...
  8. N

    Feynman Diagrams, are these allowed?

    These are my attempts, I have found two possibilities for each, but have no idea if they're 'legal'... Thanks in advance!
  9. LCSphysicist

    I General relativity, Electromagnetism and Feynman Diagrams

    We are discussing the introduction to Einstein field equation, so he start talk about the linearity in Newtonian gravity and the non linearity in GR. But there is somethings I am missing: > " (...) in GR the gravitational field couples to itself (...) A nice way to think about this is provided...
  10. 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...
  11. John Greger

    A What are some example Feynman diagrams in Yang-Mills theory?

    Hi! So I have just been studying Yang-Mills theory advanced quantum field theory. In chapter 72 of Srednicki's book Quantum Field Theory they list the Feynman rules for non-abelian gauge theory. I was asked if I could show some sample allowed diagrams but I could not.. In standard particle...
  12. S

    Books for the Mathematics of Feynman Diagrams

    Summary:: What is (are) the best book(s) to understand the mathematics of Feynman diagram? Hello, Can anyone recommend some books for the mathematics of Feynman diagram? (I don't mind if they also include the physics; in fact it may be better). Ideally I would need books that are very...
  13. M

    I Calculating 2nd Order Scattering Amplitude: Feynman Diagrams

    In the following I will try to deduce the scattering amplitude for a specific interaction. My question is at the bottom, the entire rest is my reasoning to explain how I came to the results I present. My working Let's assume I would like to calculate the second order scattering amplitude in ##...
  14. J

    A Looking Under the Hood of Feynman Diagrams

    I'm currently working my way through Griffith's Elementary Particles text, and I'm looking to understand what's going on with the underlying Hilbert space of a system described using a Feynman diagram. I'm fairly well acquainted with non relativistic QM, but not much with QFT. In particular, I'd...
  15. saadhusayn

    Calculating effective action at two loops

    Does this mean that the expression for the above vertex is $$ -\frac{g}{2}\epsilon^{abx}\epsilon^{cdx}\int d\tau \langle A_{a} (\tau) A_{c} (\tau)\rangle \langle Y^{i}_{b} (\tau)Y^{i}_{d}(\tau) \rangle $$
  16. RicardoMP

    A Trace of a product of Dirac Matrices in a Fermion loop

    I'm working out the quark loop diagram and I've drawn it as follows: where the greek letters are the Lorentz and Dirac indices for the gluon and quark respectively and the other letters are color indices. For this diagram I've written...
  17. R

    I Calculating a particular amplitude with Feynman diagrams

    So I’m trying to compute the probability amplitude of an electron with momentum p1 and a positron with momentum p2 annihilating into a photons with momenta q1 and q2. My question is how do you use Feynman diagrams to calculate the first and second order expansions (seen in the third image)? I...
  18. A

    A Feynman diagrams strong process

    Hello everybody! I have to write the Feynman diagrams for the process ##\pi^- + p \rightarrow \Lambda_c^+ + D^-##. It is a strong process since all the quantum numbers are conserved. I have attached my attempt, is it correct? Thank you all in advance!
  19. D

    B What are Feynman Diagrams and how do they help explain Quantum Electrodynamics?

    I'm new to QED, so I want to have a general grasp of what's going on. I just want to understand it conceptually. Can anyone explain it in a way so a layman can understand?
  20. A

    Mathematica Calculating traces with FeynCalc

    Hello everybody! I need a little help with FeynCalc. I think the problem is really simple but I can't find how to fix it. I want to evaluate a trace coming from a Feynman diagram. Since the particles are all massless, I want to impose the condition on the momentum ##p^2=k^2=p'^2=0##. I've...
  21. A

    Amplitude with Feynman diagrams and gluon propagators

    The term which is relevant for the calculus is: $$ \bar u(p) \gamma^\alpha \frac{1}{\displaystyle{\not}p+\not k} \gamma^\nu \frac{1}{\displaystyle{\not}p'-\not k} \gamma^\beta v(p') \frac{k_\alpha k_\beta}{k^2} $$ $$ \bar u(p) \displaystyle{\not}k \frac{1}{\displaystyle{\not}p+\not k}...
  22. A

    A Can we create a random variable using QED effects?

    Quantum Electrodynamics (QED) has some observable effects such as the lamb shift, which is mainly caused by the vacuum polarization and the electron self-energy. These effects contribute to the "smearing" of the electron in an unpredictable manner, other than the uncertainty we already have...
  23. fluidistic

    Solid State A guide to Feynman diagrams in the many-body problem

    I'm trying to go through Mattuck's book "A guide to Feynman diagrams in the many-body problem", the Dover's 2nd edition book. I have read that apparently it has been criticized for being way too easy. I'm having an extremely hard time going through the 3rd chapter, let alone the 4th! I feel...
  24. F

    I Complete list of Feynman diagrams

    Is there an on-line list of all possible Feynman diagrams for all the known particles?
  25. 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...
  26. 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...
  27. P

    A The Optical Theorem for Feynman Diagrams

    In Peskin's textbook section 7.3 The Optical Theorem for Feynman Diagrams(Page233), he said it is easy to check that the corresponding t- and u-channel diagrams have no branch cut singularities for s above threshold. But I can't figure out how to prove it. Can angone help me? Thanks!
  28. C

    A How to relate the expansion term to Feynman diagrams

    I learn quantum field theory using the book of " quantum field theory in a nutshell" by A. Zee. But I am confuse when I read the content about the "baby problem" at the beginning of "1.7 Feynman Diagrams". In that section, author get the term of order λ and [J][/4] by -(λ/4!)[(d/dJ)][/4]...
  29. 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...
  30. 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?
  31. 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...
  32. P

    I Feynman Diagram-Momentum conservation in primitive vertex

    In the first Feynman diagram, an electron comes in, emits a photon and then leaves. Is this an allowed process? Because if you rotate the diagram by 90o, the diagram should be just as valid, but it doesn't seem to be since it would violate the law of conservation of momentum. So is the...
  33. D

    I Confused about Feynman diagrams

    Hi. I'm self-studying particle physics.Just been looking at some questions where a reaction is listed and the questions asks to draw a Feynman diagram for the reaction and state which force is involved. I have the answers but they all seem so random and I would like to know how to decide which...
  34. C

    I Software for calculating Feynman diagrams

    I'd appreciate it very much if someone told me if there is any free software to (draw and) calculate the amplitudes of simple (tree and one loop) Feynman diagrams. I'm hesitating because I don't know if this is the right place to ask. If it's not, I apologize in advance.
  35. L

    A How does one find the Feynman diagrams?

    I'm studying Quantum Field Theory and the main books I'm reading (Peskin and Schwartz) present Feynman diagrams something like this: one first derive how to express with perturbation theory the n-point correlation functions, and then represent each term by a diagram. It is then derived the...
  36. N

    I Common interaction vacuum for QED + QCD?

    Hello, I know QED and QCD as isolated theories but now I thought about particle interactions with QED and QCD processes (like fpr proton-antiproton scattering). But I'm not sure how to interpret this mathematically. As I understood my Feynman diagrams are nothing more like pictures for the...
  37. 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...
  38. S

    A Deducing decay processes and Feynman diagrams using Lagrangian and conservation laws

    The decay processes of the ##W## bosons are completely governed by the charged current interaction terms of the Standard model: $$\mathcal{L}_{cc} = ie_{W}\big[W_{\mu}^{+}(\bar{\nu}_{m}\gamma^{\mu}(1-\gamma_{5})e_{m} + V_{mn}\bar{u}_{m}\gamma^{\mu}(1-\gamma_{5})d_{n})\\...
  39. V

    Drawing the quark flow diagram for proton-pion interaction

    Homework Statement I am given the following interaction, $$\pi^-+p\rightarrow \pi^++\pi^-+n,$$ and asked to draw the Feynman (quark flow diagram). Homework Equations None; just baryon number conservation, quark flavor conservation, etc. The Attempt at a Solution First, as baryon number and...
  40. ChrisVer

    A QFT phi3 Feynman diagrams and correlation function

    I have some difficulty understanding how to go about with this problem: I came up with several graphs, you can see them in the attached picture (they are up to ~g^4 order). I am not sure about the self-interaction diagrams, but I think they are considered in the connected graphs (they are not...
  41. binbagsss

    I Scattering, 4 point correlator, number of distinct Feynman diagrams

    In order to compute the scattering probability that two particles of type 1 (associated to ##\phi_1(x)##) which come from the far past with the momenta ##p1## and## p2##, to scatter and evolve into two particles of type 2 (associated to ##\phi_2(x)##) with the momenta ##p3## and ##p4## , I am...
  42. T

    A Help with Feynman diagrams involving Majorana Fermions

    Hello everyone, I am trying to compute the ΔF=2 box diagrams in SUSY with gluinos. The relevant diagrams are the following: I want to use the Dirac formalism and NOT the Weyl one. So, the only reference that I have for Feynman rules with Majorana spinors is the old but good SUSY review from...
  43. S

    A Feynman diagrams for ##e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}##

    Consider the process of electron-positron annihilation into muons as given by $$e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}.$$ The Feynman diagrams for this process to lowest-order are given by This is an s-channel diagram.Why are there no t-channel or u-channel diagrams for this process?
  44. woody stanford

    I Building a List of Feynman Diagrams

    Back again. This time I'm looking to build a small catalog of Feynman diagrams for my own use (and when I'm done to put it on the Internet in PDF format). I need your help to get a list of URLs together that I can download the required PDF's off the internet, bring them into Illustrator and have...
  45. J

    A Srednicki's QFT: Feynman Rules and Feynman Diagrams

    I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. Link to the book: The path integral for the phi-cubed theory is equation 9.11 in the book. Please read that. I get the...
  46. N

    I Lagrangian and Feynman diagrams

    Hello, Consider the the following Lagrangian of the $\phi ^4$ theory: $$\begin{align*} \mathcal{L} = \frac{1}{2} [\partial ^{\mu} \phi \partial _{\mu} \phi - m^2 \phi ^2] - \frac{\lambda}{4!} \phi ^4 \end{align*}$$ Now I'm interested in Feynman diagrams. 1. The second term gives the...
  47. 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...
  48. 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.
  49. 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##...