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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Michio Kaku: non-renormalizable Einstein's theory of gravitation, nonzero counterterm at 2-loop, and Heisenberg

In p.9 of Michio Kaku book Introduction to Superstrings and M-Theory-Springer (1998), he said General relativity is not renormalizable. Computer calculations, for example have now conclusively shown ...
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Complex Fields, Propagators, Wick's Theorem and Feynman Diagrams

I'm having quite the problem connecting all these concepts, so apologies for the lengthy post. Complex Fields and Feynman propagators Let $\psi$ denote a complex field. Then, after quantization, we'll ...
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Antisymmetrization rule in Feynman diagrams of QED

I am having trouble understanding the Antisymmetrization rule given in Griffith's book for the calculation of amplitude which states that "include a minus sign between diagrams that differ only ...
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What are “combinatorial factors” in the Lagragian?

I'm reading "Renormalization" by John C. Collins and in the fifth chapter "Renormalization" under the subchapter 5.6 "Relation to $\mathcal L$", he defines the Lagrangian ...
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Negative energy quanta vs antimatter approach

Consider 2 physical scenarios: $t_{-1}$ $t_0$ $t_1$ Sc.1 electron and positron approached electron and positron annihilated photons emitted Sc.2 electron is free electron emits some photons ...
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Feynman Diagram for proton-proton and for neutron- neutron [closed]

What are the Feynman diagrams for these two reactions? $$p+p \to p+p + \pi^+ + \pi^- + \pi^0 \\ n+n \to \pi^+ + \pi^- + \pi^0$$
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3-point amplitudes in QED

I am currently interested in 3-point QED amplitudes that involve both a photon and massless fermions. In the "limit" of real momenta these 3-point amplitudes vanish. However if we consider ...
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Ward Identity for Pair Pair Annihilation

The following Feynman Diagrams for the process $e^++e^-\to\gamma+\gamma$ are: Knowing this I wrote the amplitude matrix: $$M = -e^2\epsilon^{*}_{\mu}(p_3)\epsilon^{*}_{\nu}(p_4)\bar{u}(p_2)\left[\...
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Nonlinear superposition and self-interaction in classical field theory

I am learning QFT (in a path integral formalism) and one thing I'm struggling with is that self-interaction is supposed to be a quantum phenomenon, not apparent in classical non-linear field theory. I ...
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Feynman rules to spinor helicity

The following amplitudes of the 3-gluon vertex are obtained only from momentum conservation (shown in Quantum Field Theory and the Standard Model, Schwartz): $$M^{+++}=C^{abc}\frac{1}{\langle12\rangle\...
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How to draw Feynman diagram of quark decaying to more than three quarks (weak), and tell if it's Cabibbo-allowed/supressed?

I have problems when it comes to drawing Feynman diagrams that involve weak decays creating more than two quarks. So I hope one of you can help me clarify. let's consider the following problem: Will ...
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Yang-Mills self-energy

I am trying to write the diagrams associated with the self energy of a Yang-Mills field. I have already computed the Feynman rules for the propagators and for a vertice of: 3 gluons; 4 gluons; 2 ...
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Adjoint spinors in Feynman diagrams

I am reading through Griffiths textbook "Introduction to Elementary Particles" and I am in the middle of the chapter on Quantum Electrodynamics and Feynman Rules for his diagrams. There is ...
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Clarifying Griffiths syntax when solving Feynman Diagrams

In Griffiths textbook "Introduction to Elementary Particles", he details how to use Feynman diagrams and walks through some examples of solving some essential particle interactions. The ...
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Should quarks be grouped together in Feynman diagrams?

I have a questions regarding Feynman diagrams when it involves hadrons. I think the easiest way is considering this reactions: 1) $\Lambda_{c}^{+} \rightarrow p+\bar{K}^{0}$ I need to draw the ...
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Contractions of probability amplitude in quantum field theory

Given a Lagrangian $$\mathcal{L}=\frac12(\partial_\mu \phi(x))^2+\frac12m^2 \phi(x)^2-\frac{\lambda}{4!} \phi(x)^4$$ The probability amplitude in each order is given by: $$A=(2\pi)^3 (2E_q)^{1/2} (...
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Can the $W^+$ boson couple an antistrange quark decaying into an antiup quark?

I am trying to figure out the Feynman diagram for the fully hadronic $K^+$ meson decay $K^+ \rightarrow \pi^+ + \pi^0$. I have drawn out my attempt below, but in order for this to work, I would need ...
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Simplicity of the electron positron anhilation amplitude at the tree level $e^+ e^-\rightarrow \gamma \gamma$

The calculation for the electron positron annihilation to 2 photons amplitude takes up 5 pages in $\LaTeX$, and the answer is astonishingly simple $$\mathcal{M}=-4g_e^2.$$ Even Griffiths notes this ...
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Graviton-graviton scattering in tree level. Based on a talk by Bryce DeWitt

In this talk given by Bryce DeWitt, at page 6 he mentions a problem he gave to one of his PhD students. The problem is to compute the graviton-graviton scattering amplitude in tree level approximation....
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Number of possible Feynman diagrams at a given perturbative order

In perturbative quantum field theory, all amplitudes for processes $\sum \text{in}\to \sum \text{out}$ involving particles that interact according to a certain interaction Lagrangian $\mathcal L_I$ ...
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QM is Feynman path ensemble - can QFT be viewed as Feynman field ensemble?

While classical mechanics uses single action optimizing trajectory, QM can be formulated as Feynman ensemble of trajectories. As in derivation of Brownian motion, mathematically it is convenient to ...
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Feynman diagrams in the Yukawa theory

I'm trying to find out the best method to find the Feynman diagrams which appear in the Yukawa theory $L_{int} = -y \bar{\psi} \psi \phi $ in the 4 point Greens function $g^{(4)}$ with external scalar ...
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What does $k$ stand for in self-energy of renormalization?

I'm reading "Renormalization" by John C. Collins, and it doesn't introduce the $k$ term, but uses it anyway. Here is an excerpt for clarification: "When all components of $k^\mu$ get ...
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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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54 views

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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61 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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126 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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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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