feynman diagram Definition and Topics - 83 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. G

    I Photon-Photon Feynman Diagram

    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?
  2. U

    Check if the amplitude of the process ##\mu \mu \rightarrow H H## is correct

    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...
  3. 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} =...
  4. 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...
  5. steve1763

    A Feynman Diagrams associated with the generating function of this free scalar field Lagrangian

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

    Decay Feynman Diagrams

    Δ ++ → p + π0 Ξ - → Λ0 + π-
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. C

    Feynman diagram

    Homework Statement Homework Equations The 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]
  13. 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...
  14. 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?
  15. 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...
  16. 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...
  17. 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...
  18. 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?
  19. 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...
  20. Safinaz

    I Sunset 2-loops diagram

    Hi all, I'd like to calculate the self energy amplitude of the following sunset diagram (take the middle for instance ) can any one help me in distributing the momentum on the internal propagators ? Best
  21. 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}##...
  22. 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...
  23. N

    A Box diagram calculation (Kaon mixing)

    I am trying to calculate box diagram of Kaon mixing by follow the "CP Violation" book. Now, I arrived at equation (B.8) and I have problem with getting equation (B.12). F(x_\alpha,x_\beta)=\dfrac{1}{(1-x_\alpha)(1-x_\beta)}(\dfrac{7x_\alpha...
  24. H

    Intuition for divergences in sunset diagram

    What is the intuition behind divergences for the sunset diagram? I know that there is quadratic divergence by why no quartic divergence or higher?
  25. 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...
  26. H

    Vacuum diagrams vs. tree diagrams vs. loop diagrams

    Could someone please tell me the difference between tree diagrams and loop diagrams? If I'm thinking correctly tree diagrams are before contracting? Also how do vacuum diagrams fit into the picture? Thanks!
  27. 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...
  28. C

    Cuts of a Feynman diagram and the massless limit

    Consider a ##j## point all massive leg one loop polygonal Feynman diagram ##P## representing some scattering process cut on a particular mass channel ##s_i##. Invoking the relevant Feynman rules and proceeding with the integration via dimensional regularisation for example gives me an expression...
  29. N

    How to compute the vertices from interaction lagrangian?

    Hello all, If I am having the the effective lagrangian which is actually free + interaction lagrangian (obtained from the minimal substitution for pseudoscalar and vector mesons). then how to compute the vertices of the interaction ? I have taken into consideration of all symmetry breaking...
  30. AlanKirby

    How can e-e+ possibly go to ZZ?

    Hi there, my question is the following. If an electron and positron annihilate, how can they result in ZZ? The issue i'm having is that due to charge conservation, the exhange particle can't be W- or W+. It also can't be a photon since the Z's don't have electrical charge to couple to. It also...