Questions tagged [feynman-diagrams]

A diagrammatic technique introduced by Richard Feynman to describe the quantum behaviour of subatomic particles and their interactions. Do not use for general questions on diagrams that are not of the Feynman kind.

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Why are there infinitely many Feynman diagrams for any particular reaction?

In Griffith's Intro to Elementary Particles book, he wrote there are infinitely many Feynman diagrams for any particular reaction! Why is this true? Take for example Moller scattering that ...
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Perturbation theory development for the ground state of the QM particle in the box with a centered dirac-delta spike

In the course of a discussion in the chat there emerged an interesting problem, namely a particle in an infinite well with an additional Dirac-delta function spike of scalable hight: $$ H = -\frac{\...
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How to search Feynman diagrams for entanglement [closed]

This question is partly about physics, partly about love -- but I don't believe there's a Stack Exchange for the later :) My girlfriend is a PhD physicist who finds the notion of entanglement very ...
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Feynman diagrams: from QFT to condensed matter

I studied Feynman diagrams in quantum field theories and I'm going to study them in the context of condensed matter physics. In this post Books for Condensed Matter after Ashcroft/Mermin, two books ...
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Why this self-loop diagram is not included in $\phi^4$-theory of Peskin & Schroeder?

Consider a $2\rightarrow2$ scattering process in $\phi^4$-theory. On p. 326 in the book of Peskin & Schroeder, they consider the 3 1-loop corrections in the parenthesis: My question is: Why don't ...
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How do one find the first correction order of $\lambda$ for scattering cross section?

I have a lagrangian $\mathcal{L}=\mathcal{L_0+\mathcal{L_1}}$, where $\mathcal{L_1}$ is a perturbation given by:$$\mathcal{L_1}=-(1/3!) \lambda \phi^3-(1/4!) \lambda \phi^4 $$ and$$\mathcal{L_0}=-\...
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122 views

Summation of an exponential operator on quantum amplitude

For a quantum Dirac field interacting with a classical EM field, one can (through the Quantum Dynamical Principle) write the vacuum transition amplitude as $$\langle0_+|0_-\rangle=\exp\left[ie_0\int ...
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125 views

Simple explanation of a particular diagrams of Feynman [closed]

In relation to this question posed on the website TeX.SE. I am curious to know the use in Physics of green functions about the signs of feynman diagrams with fermionic fields. I have not understood ...
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34 views

The different limits of a scattering process

Let's assume I have a process of some sort ($e^-e^+\rightarrow e^-e^+$ / $e^-e^-\rightarrow e^-e^-$ / etc) and I calculated its unpolarized differential cross section using no assumptions at all (...
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164 views

Quantum Scalar Field Theory with cubic and quartic interaction

If I have a scalar Lagrangian with and interaction term given by cubic and quartic terms (so a scalar theory + $φ^3+φ^4$ interaction), what are the possible divergent 1PI diagrams at one and two loops?...
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53 views

Are there Rules for 'Splitting' Feynman Diagrams?

I was talking with a mathematician colleague and promised to look up a concept in QFT for them but am not sure what they were referring to. They were referring to rules named after two people (both ...
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What is the closed form of the following integral?

I want to know the closed form of the following master integral in (any) $D$ dimension \begin{equation} \int\frac{d^D k}{(2\pi)^D}\frac{1}{k^2(k+r)^2(k+p)^2}. \end{equation} The references that I can ...
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97 views

Feynman Parameters vs Passarino-Veltman reduction

I have computed the following one-loop integral: $$\int \frac{d^dp}{(2\pi)^d} \frac{p^{\mu}p^{\nu}}{(p+k)^2p^2}.$$ Using both Feynman Parameters and the Passarino-Veltman reduction. However, while I ...
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Why can't a particle interaction $A + B \rightarrow C$ conserve energy and momentum at the same time?

I learned that in the Feynman diagram for electron photon scattering, the intermediate particle represented by the middle solid line must be a virtual particle because it violates energy-momentum ...
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103 views

Physics Meaning of Trace Technology in QED [closed]

As it pointed out on page 133 of Peskin and Schroeder, any QED amplitude involving external fermions, when squared and summed or averaged over spins, can be converted to traces of products of Dirac ...
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53 views

u-channel in $gg \rightarrow u\bar{u}$

I've seen that for the QCD process $gg \rightarrow u\bar{u}$, where $g$ is a gluon and $u, \bar{u}$ are the up quark and the corresponding antiquark, there is s, t and u channels. I perfectly ...
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120 views

Optical theorem in $\phi^4$: which poles contribute to discontinuity in Feynman amplitude?

Section 7.3 ("The Optical Theorem") in Peskin and Schroeder's QFT text contains a leading order verification of the optical theorem in $\phi^4$ theory by calculating the (discontinuity across the ...
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Feynman Rules from Lagrangian with charge conjugation matrix

I'm dealing with a doubly charged scalar singlet that interacts only with the right-handed muon as follows, $$\mathcal{L} = \lambda \psi_{R}C\psi_{R} \phi^{++},$$ where $\lambda$ is the coupling, $\...
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Why don't very high order Feynman diagrams contribute significantly?

In a particle physics lecture I had today it was stated that the magnetic moment, $g$, is not quite equal to 2, and the difference is accounted for by QED. Later it was stated that we can see this ...
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Faster ways of computing feynman diagrams

Obviously the machinery of QFT allows us to calculate processes, such as QED diagrams, to great precision, and whilst it is effective, it seems there are many processes that make calculations (say by ...
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26 views

Effective potential and radiation corrections

I'm a bit confused on the idea of adding corrections to the classical potential of $\phi^4$ theory in QFT. From what I understand is that one should add corrections to the potential in order to ...
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When can you simplify the $W$ boson propagator?

I have seen in several sources that the propagator of the $W$ boson is: $$\frac{- i \left( g^{\mu\nu} - \frac{P^\mu P^\nu}{m_W^2} \right)}{p^2 - m_W^2} . $$ But then in some calculations (usually ...
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223 views

What happens in the Hartree and Fock diagrams?

I am trying to understand the Hartree and Fock diagram shown in the picture. To understand it a assume there is an electron entering and leaving at the tail of the tadpole (Hartree diagram) and an ...
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108 views

Imaginary part of vacuum polarization tensor

I deal with vacuum polarization diagram calculation with help of QED by Landau et al. and I would like to understand one interesting statement. I know how to compute $\Pi_{\mu\nu}(k)$ via dimensional ...
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43 views

How to know what type of diagram contributes to a two-to-two process?

There are 3 types of diagrams that can contribute to a two-to-two process; the $s$-channel, $u$-channel and $t$-channel. How do I know what diagrams can contribute to a process? I know that in QED, ...
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95 views

Cutkosky's rule for vertex correction

I don't understand how to evaluate the diagram for electron-photon vertex with help of Cutosky's rule: According to the rule, one should cut diagram "in the middle". I denote final state as F and ...
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How to determine the squared average amplitude for $\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$?

I have the following charged current interaction, at quark level, by the process: $$\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$$ By assuming that the energy is such that I can neglect the lepton and ...
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177 views

Superficial degree of divergence in $\lambda\phi^4$

Ryder at the beginning of the chapter about renormalization defines the "superficial degree of divergence" of diagrams in $\lambda \phi^4$ theory. I'll recap the derivation. A diagram in $\lambda\phi^...
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Sign ambiguity when going from position to momentum space evaluating Feynman diagrams

When calculating a simple diagram I came across an ambiguity in the conservation of momentum, i.e. it seems to me that the particle could come out of the process with opposite momentum with respect to ...
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Manipulation of momentum factors in Feynman integrals (solved)

My current understanding: Consider a massless Feynman graph with propagators of the form $1/p^2$ and some momentum factors in the numerator. Now consider a vertex, which for simplicity of notation is ...
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162 views

Higgs Feynman Diagrams

We have been told to compute the amplitude of these diagrams: I am struggeling with some basic points( I've only computed QED diagrams such as Bhabha scattering). Do you use $\epsilon$ for the ...
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Muon neutrino interacting with nucleon's quarks

I'm considering the muon neutrino/anti-quark interaction with the nucleons of ice in the IceCube experiment. The purpose is to decide which antiquarks are $\bar{q}$ and $\bar{q}'$. I have the ...
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Meson scattering amplitude in the linear sigma model

I am trying to calculate scattering amplitudes with linear sigma model Lagrangian, given as $$\mathcal L= \frac{1}{2}(\partial_{\mu}\sigma)^2+\frac{1}{2}(\partial_{\mu}\vec{\pi})^2-\mathcal U(\sigma,\...
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314 views

Propagator for W boson

I've found in different literature that some write the propagator for the W boson as $\frac{g_{\mu\nu}-\frac{k_\mu k_\nu}{M^2_W}}{k^2-M^2_W+iM_W\Gamma_W}$ and others like $\frac{g_{\mu\nu}-\frac{k_\mu ...
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54 views

Muon neutrino and down quark interaction diagram

My questions concerns the IceCube experiment, in particular, the interaction between muon neutrino and the down quark. I've drawn the following Feynman diagrams: Are both diagrams correct? Can I say ...
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Is this feynman diagram possible? $e^- + e^+ \to \nu_\mu + \bar{\nu}_\mu$

I am starting to learn about Feynman diagrams and I have been told that flavour has to be conserved at vertices in the case that the exchange particle was neutral. Since here the exchange particle is ...
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Could this feynmann diagram happen on its own? $e^- \to W^- + \nu_e$

I am starting to learn about Feynman diagrams and I wonder if this reaction could happen as a physical process on its own, as opposed to part of a more complicated diagram: $e^- \to W^- + \nu_e$ ...
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179 views

Completeness of an electron-electron-scattering in the Feynman diagram

During an electron-electron-scattering in any case the electrons change their directions and by this undergo accelerations. Shouldn’t the electrons emit photons in this time, loosing a part of its ...
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An involved Feynman integral

Working with QCD, I have found the following integral from Feynman diagrams to solve $$ I(p)=\int\frac{d^4p_1}{(2\pi)^4}\int\frac{d^4p_2}{(2\pi)^4}\frac{1}{p_2^2-m_0^2} \left(\frac{p\cdot p_1-p_1\cdot ...
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Approximations in QFT and the problem of convergence

I would like to understand the problem of the convergence/divergence of the series appearing in QED: my question is inspired by a great article of John Baez, which can be found online. On the page 23 ...
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Feynman diagrams: How to find factors for external particles

In class we learned how to compute Feynman rules from the Lagrangian. I know how to find propagators and vertices. But is there a general rule for external particle lines?
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229 views

One-loop diagram in scalar field theory

We see that this loop contain particle with momentum $p+k$ and anti-particle with momentum $k$. But I fall into contradiction because the Feynman integral corresponds to this loop (see the book http:...
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162 views

Lagrangian with quadratic interaction

A real scalar field has Lagrangian $L=L_0+L_1$, where the free part $$L_0=-\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2$$ and the interaction term $$L_1 = + \frac{1}{2}g\phi^2.$$ I have two ...
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Is it possible to define Feynman diagrams in curved space-time?

I have a very simple question: "Is it possible to talk about Amplitudes and Feynman diagrams assuming a different background than the usual Minkowski one? Let's assume for example that the background ...
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One-loop correction to triple gluon vertex in QCD

I'm trying to calculate a one loop correction to the 3 gluon vertex, which is given by a circular correction, and another that's due to the 4 gluon vertex. However I'm unsure how the ghost fields ...
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Can the Hermitian conjugate of a column vector still be column vector?

From what I understand, contravariant vectors are represented by column vectors, and covariant vectors are row vectors. So for a QED current, say $j ^ { \mu } = \overline { \psi } \gamma ^ { \mu } \...
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Feynman rule for 3-gluon vertex

I want to obtain the Feynman rule for the 3-gluon vertex, but looking at the result I don't really know how to tackle it. The relevant term in the Lagrangian is \begin{equation} \mathcal{L}_\text{...
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368 views

Compton Scattering Lowest Order Feyman Diagram

I have some trouble understanding the lowest order feyman diagrams for compton scattering. Does two feyman diagrams mean that compton scattering can happen through two processes? What is the ...
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196 views

Equivalence between $t$ and $u$ channels

Reading about QFT diagrams, I've seen examples like Bhabha scattering where the channel $u$ wasn't necessary due to the final states are distinguisable for being made of the different particles and ...
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Can a black hole ever be the output of a Feynman diagram in momentum space?

For a Feynman diagram representing a collision, particles come in from infinity with certain momenta, collide and then go off to infinite with other momenta. At collision vertices we integrate over ...