feynman diagrams Definition and Topics - 25 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. 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...
  2. M

    I Consfused about the workflow for calculating scattering amplitudes with 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 ##...
  3. saadhusayn

    Calculating effective action at two loops

    Does this mean that the expression for the above vertex is $$ -\frac{g}{2}\epsilon^{abx}\epsilon^{cdx}\int d\tau \langle A_{a} (\tau) A_{c} (\tau)\rangle \langle Y^{i}_{b} (\tau)Y^{i}_{d}(\tau) \rangle $$
  4. 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...
  5. 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!
  6. 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...
  7. 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}...
  8. 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...
  9. Cardinalmont

    B Feynman Diagram 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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.
  14. 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...
  15. N

    I Common interaction vacuum for QED + QCD?

    Hello, I know QED and QCD as isolated theorys 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...
  16. 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...
  17. 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})\\...
  18. 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...
  19. 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...
  20. 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.
  21. 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...
  22. 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...
  23. H

    Using Feynman rules to calculate amplitude

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

    Vector QED Feynman rule

    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: $$ Z + e^- \rightarrow Z + e^- + v. $$...
  25. G

    Lagrangian of fields from Feynman diagrams

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