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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Wick's theorem, contracting field operators at the same point

I want to calculate the amplitude for nucleon meson scattering $\psi \varphi \to \psi \phi$ in scalar Yukawa theory, with interaction term: $$H_{I} = g \int d^{3}x \psi^{\dagger} \psi \varphi.\tag{3....
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LSZ formula and connected Green functions

My question is relatively simple. In the LSZ formalism, it is said that S-matrix elements correspond to on-shell limits of Green's functions. On the other hand, what people usually do is that they ...
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Problems understanding the BCFW recursion formula

I am currently reading through the chapter about the spinor helicity formalism in Schwartz Quantum Field Theory and Standart Model. In the chapter 27.6 (On-shell recursion) the author introduces the ...
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Is a Feynman vertex valid only if all its rotations are?

Consider a toy universe with only the following particles/fields: A lepton $\psi$, with antiparticle $\bar \psi$. A vector boson $A$ (self-conjugate), that does not interact with itself. Based only ...
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62 views

What is an $n$-gluon amplitude?

What exactly is meant when we speak of an n-gluon amplitude? For example, in case of $n = 6$: Does the $6$-gluon amplitude refer to all possible diagrams that involve six gluons (which means e.g. ...
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Why do we factor out a momentum-conserving delta function in a 1-loop 1PI diagram in $\phi^4$ theory?

I do not understand the meaning of factoring out $(2\pi)^4 \delta ^4(p_1 - p_2)$, surely the delta function will have argument zero ($p_1 = p_2$) and should consume one integration and $(2\pi)^4$ ...
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Elastic Proton-Proton Scattering at tree level

Hello im trying compute the Cross section of an elastic proton-proton scattering and my results are beyond terrrible and i can't figure out where my mistakes lie. I'm going to describe what i tried to ...
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List of amplitudes at 1-, 2-loops for scalar field theories

I would like to know if there is any database/reference which has an explicit list of all the amplitudes that are known, at least in the more common scalar field theories like the $\phi^4$ and $\phi^3$...
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Why is the $Z$ resonance cross section so much larger for hadrons? [duplicate]

The image shows experimental data for the ratio of cross sections $$R=\frac{\sigma(e^+e^-\rightarrow\text{hadrons})}{\sigma(e^+e^-\rightarrow\mu^+\mu^-)}.$$ I am wondering why $R$ is so large for the $...
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Do resonances always correspond to on-mass-shell virtual particles in tree-level Feynman diagrams?

I understand that the main consensus on this site is that virtual particles should not be interpreted too physically and simply correspond to terms in a perturbative expansion, so please forgive my ...
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Are there Feynman rules to calculate form factors in QED?

I just learned about Feynman rules to calculate scattering amplitudes in QED. I was looking into the anomalous magnetic moment and was wondering how I could 'translate' these Feynman diagrams to ...
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Feynman rules for Nucleon-Nucleon Interaction with Tensor Coupling

Hello im trying to Compute the Cross section of an elastic Nucleon-Nucleon scattering and i don't know what to make of the following Lagrangian: \begin{equation} \mathcal{L}_{\rho N N}=-g_{\rho} \bar{\...
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Conservation of momentum for a 3-point amplitude

When talking about 3-point amplitudes (e.g. three gluons) I`ve come across the fact, that if we have three lightlike 4-momenta $p_1,p_2$ and $p_3$ they should satisfy $$p_1^{\mu} + p_2^{\mu} + p_3^{\...
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Coefficients in Feynman Diagrams

Consider the 4-point correlation function, $G(x_1,x_2,x_3,x_4)$, in $\phi^4$ theory. Let us consider the term which is $\propto \lambda^2$, represented by the following Feynman's diagram: According ...
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Calculating Wilson coefficients quickly

I am currently trying to compute the Wilson coefficients for the different amplitudes in scalar field theories, where these are the coefficients $\mathcal{W}_{pq}$ defined by $$ \mathcal{M}(s,t) = \...
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Possible mistake in Peskin and Schroeder

Attached here is a picture from Peskin and Schroeder, page 342, section 10.5. If I understand it correctly, the "shifted momentum variable" $l$ should be equal to ($k$ + independent of $k$ ...
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Probabilities of $ \Omega^- $ baryon decay

The $ \Omega^- $-decay can occur in a few different ways. According to this document (page 3, $\Omega^−$ DECAY MODES), the three most probable decays are \begin{align} \Omega^- &\to \Lambda^0 + ...
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How to determine amplitude of compton scattering using Feynman rules?

I am currently studying from Griffiths' introduction to elementary particles. I started reading about the Feynman rules for caclulating scattering amplitudes, and while I understood them for the ...
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Scattering amplitudes of Higgs boson production in weak boson fusion

I want to write the scattering amplitude for this diagram using feynman rules in unitary gauge. I will drop the prefactors, since they do not bother anyway. Here is what I ended up with: $$ \mathcal{M}...
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Cancelling UV divergences with IR divergences

My main question is the following: Are there certain QFT's in which for all Feynman diagrams the UV divergences cancel the IR divergences, leaving only a finite result for each diagram. While ...
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135 views

Feynman diagram for the decay $\tau \rightarrow \nu_{\tau}\pi^+\pi^-\pi^-$

$$\tau \rightarrow \nu_{\tau}\pi^+\pi^-\pi^-$$ This is a possible decay mode of the $\tau$ lepton (see Wikipedia). Given that a neutrino is present this must be the weak interaction and therefore we ...
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54 views

Trace evaluation in inverse muon decay

Applying Casimir´s trick when averaging over the the initial and summating over the final spin states in the inverse muon decay yields (Griffiths, example 10.1) among others the following trace $$ \...
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Contraction of 4-dimensional epsilon tensor with four-vector components

Evaluating a feynman diagram via the trace method I encoutered the term $$ p_\alpha p'_\beta k_\mu k'_\nu\cdot \epsilon^{\alpha\beta\mu\nu} $$ where $\epsilon^{\alpha\beta\mu\nu}$ denotes the 4-...
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What is the mass dimension of a tree diagram?

Looking at: Why do all Feynman diagrams with same number of external legs have the same mass dimension? [Qmechanic (https://physics.stackexchange.com/users/2451/qmechanic), Why do all Feynman diagrams ...
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Is there a chance (in QED) that two electrons move from two spacetime points to two other points without interacting?

Is there a "zeroth-order" effect in quantum field theory (QED) that two electrons move from two fixed spacetime points to two other fixed spacetime points without the presence of virtual ...
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Feynman diagram for double-bubble vacuum graph in $\phi^4$ theory

I was trying to do an exercise from the book "QFT for the Gifted Amateur" by Tom Lancaster. It involves computing the momentum space amplitudes of some Feynman diagrams. I was trying to ...
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Is the $A Z$ propagator transverse?

I know that the photon propagator is transverse to all orders in perturbation theory as it must be due to the Ward identities. But is the $A Z$ propagator (where $A$ stands for the photon), presented ...
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3answers
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Is there a motion picture of sub-atomic particle collisions?

We're all familiar with these pictures describing the collision between two sub-atomic particles. I was thinking about Richard Feynman's description of an anti-proton as a proton that's simply moving ...
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Is there a fundamental reason why in the Standard Model, there is no Feynman rule for a vertex with more than 4 legs?

In Standard Model, there are vertices with 3 legs (example: $W l\nu$) and with 4 legs (example: $WWWW$). Is there a fundamental reason why in the Standard Model, there is no Feynman rule where a ...
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1answer
32 views

Mixture os $W$ boson with charged Goldstone boson

Is a propagator like this possible in the Standard Model? In fact, there is a term of the form $i m_W (W_{\mu}^- \partial ^\mu \varphi^+ - W_{\mu}^+ \partial ^\mu \varphi^-)$ in the Lagrangian so ...
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Are the spinors one can find in the Feynman rules always solutions of the free Dirac equation?

For a given Feynman diagram one can calculate the matrix Element by translating the diagram into math using Feynman rules. In these calculations one will encounter incoming and outgoing particles (and ...
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Help with the interpretation of electron-positron pairs in Feynman diagrams for Thomson scattering, in terms of the Dirac “hole theory”

I'm studying the Dirac theory for the electron, following Sakurai's Advanced Quantum Mechanics. Before even getting to the quantization of the Dirac field, the "hole theory" of a negative ...
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How to construct Feynman diagram for decay of pseudoscalar $\phi$ meson?

I am struggling to understand the construction of the Feynman diagrams for the following decays: The answer is given as follows: I do not understand how the quark anti-quark pair in each diagram is ...
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How to construct a diagrammatic interpretation out of $Z[J]$?

I am aimed at understanding how to derive the Feynman rules out of a generating functional $Z[J]$, which depends on the set of coordinates $x=(x_1,...,x_n)^T \in \Bbb R^n$ and Grassmann variables $\...
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Do quarks annihilate into photons or virtual gluons?

I initially assumed a quark and its anti quark would annihilate into 2 photons (like electrons with positrons) and this does seem to be the case at least sometimes (e.g. For $\pi^0$s). However in our ...
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(No) Field Renormalization in $\phi^4$ theory at one-loop

What might be the physical intuition behind the fact that we don't need to renormalize the field/wave function at one-loop level in $\phi^4$ theory? I justify the field renormalization thinking "...
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CERN LHCb leptoquarks and grand unified theory

Recent CERN LHCb experiment suggests possible leptoquarks as new particles beyond the standard model may be discovered, with 3.1 $\sigma$ not the 5 $\sigma$ discovery. What are the viable candidates ...
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On the spacetime significance of Feynman diagrams (and Witten diagrams)

This post is just a thought about Feynman diagrams and their interpretation. When I draw a FD, my intention is to provide a direct way to calculate terms in a series expansion. Now, from what I ...
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Are the photons that we detect with our eyes virtual? [duplicate]

From asking several questions about virtual particles on this website, the most popular consensus (on PSE at least) seems to be that they are nothing more than a convenient way of expressing a ...
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Majorana fermions - Scattering amplitude/Feynman rules

I am looking at 4 field scattering processes ($\phi \phi \rightarrow \psi \psi$) given by the Lagrangian is \begin{equation} \mathcal{L}_i \supset \frac{\lambda_s}{\Lambda} \overline{ \psi} \psi |\...
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1answer
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Feynman loop diagram with off-shell momenta

I wanted to evaluate the Wilson Coefficients for the process $c\rightarrow su\bar{d}$ since wherever I look they seem to be always given, for the exception of Schwart's book Quantum Field theory and ...
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Feynman rules for scalar electrodynamics

The issue I have been learning perturbation theory in QFT, but due to the weird nature of the course I was attending I still haven't learned how to properly do it by Feynman diagrams. I think the best ...
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2answers
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Is it possible to create protons from photons?

I've read a few pages on related topics (e.g., here) but not found this question. Is this type of reaction theoretically possible that we know of? I know pair production creates electron and positrons,...
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Reference for scattering amplitude for $\phi^4$ at three loops

Does anyone have a nice reference for a three loop computation in scalar $\phi^4$ theory in 4 dimensions? I mean, some place where they have the computation explicitly done. I'd ask the same question ...
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Feynman Propagator

I have learned two ways of representing Feynman Propagator, which are as follows: The first method is to represent it in the form of commutation relations: $$[a^{-}(x), a^{+}(y)] = iG(x-y)$$ Where $a^{...
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Explicit example of dimensional regularization involving $\gamma^5$

I'm currently reading Collins' book Renormalization, Chapter 4. In section 4.5 he introduces $\gamma$-matrices and the trace operation in an arbitrary dimension $d$. In section 4.6 he then talks about ...
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Calculating Feynman diagram of W-Boson exchange

Hello, for my bachelor thesis I have to calculate $|M|^2$ of this Feynman diagram. However, I have no understanding of QFT so far. I was told to just look up the Feynman rules and put them to use. As ...
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Treating a mass term as an interaction

The mass term of, say, a one real scalar free quantum field theory can be treated as an interaction with $$\mathcal{L}_I= -\dfrac12 m^2 \phi^2.$$ Once that diagrams are summed to all orders of ...
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Connected diagrams and keldysh

I have seen that: In the ground state ($T = 0$) formulation of the Green’s function written in terms of operators in the interaction picture, the Green’s function reads: $$G(r,t;r',t') = -i\frac{\...
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Peskin and Schroeder's argument on Yukawa Potential

I am reading Peskin and Schroeder's QFT book and a specific section on Yukawa Potential (P121, Chapter 4). In equation 4.119, when calculating the scattering amplitude, they have two Feynman diagrams ...

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