# 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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### "Mirrored" diagrams of $n$-point functions

Suppose we are calculating the two-point function $\langle\phi(x_1)\phi(x_2) \rangle$ and we've obtained a loop diagram of the kind on the left. Will there necessarily also be a diagram as on the ...
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### Finding symmetry factors

Suppose we have a two-loop graph that looks like two balloons next to each other or stacked on top of each other. What are the symmetry factors of these graphs? Note that I'm trying to compute a two-...
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### Difference of decay amplitude and transition amplitude from initial to final state

In Zwiebachs "A First Course in String Theory" 2nd edition he states in chapter 25.2, that "the amplitude for an initial state consisting of a $\phi$ particle to turn into a final ...
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### $W$ boson self-energy

I am trying to calculate $W$ boson self-energy (radiative correction due to top quark) in order to demonstrate that $\rho$ parameter isn't exactly 1 (it's 1 in tree level). The diagram would be the ...
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### Deriving mathematical solutions from Feynman diagrams [duplicate]

So I know that we can represent mathematical expressions using Feynman diagrams, however, I wonder if we could derive mathematical solutions from a Feynman diagram. For example, if we have the Feynman ...
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### Mathematical result for one-loop diagram of $\phi^3$ theory in four dimensions

The one-loop diagram in $\phi^3$ theory in four dimensions gives the following integral (I have suppressed factors of $2\pi$) \begin{equation} \tag{0} \Gamma(s) = \Gamma(p^2) = \int {d^4 k} \frac{1}{[(...
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### Contraction of Lorentz indices in gluon propagator of QCD

In QED, the photon propagator has a factor of $g^{\mu \nu}$, and both $\mu$ and $\nu$ contract with the $\gamma$ matrix indices, which come from the fermion antifermion photon vertices on either end ...
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### Coleman-Weinberg mechanism at two-loop

I'm trying to understand how to perform the CW mechanism (http://www.scholarpedia.org/article/Coleman-Weinberg_mechanism) to scalar theories at two-loop order. More specifically how to find the ...
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### Fermi statistics in the Feynman rules for the Gross-Neveu model

I am trying to understand the Feynman rule for the 4-fermi interaction in the Gross-Neveu model. Based on this Peskin & Schroeder solution 12.2 and this and this Stack Exchange clarification, I ...
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### Can we expect some nice "conservation laws" to be hold at each vertex of any Feynman diagram?

I'm reading two textbooks: A. Zee's QFT book and Bruce Bartlett's TQFT book. In Zee's book, chapter 1 & 2 introduces Feynman diagram smoothly. Although notations are slightly different, I'll ...
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### Order of spinors in an equation for a Feyman diagram or contraction

I'm going over scattering theory in Peskin and Schroeder book, in his chapter on fermion scattering he wrote a specific contraction and the equation describing it One thing he didn't mention is the ...
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### What is the reason choosing arbitrary incoming/outgoing conventions of particles in a Feynman diagram work?

Lets consider any specific Feynman diagram for the process $A(p_1)+B(p_2)\rightarrow C(p_3)+D(p_4)$, where $p_1, p_2$ are the ingoing momenta and $p_3, p_4$ are the outgoing momenta. As I have now ...
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### Skeleton diagrams and 2-particle irreducibility

I want to derive the properties of the Luttinger-Ward functional from the 2-PI (CJT) effective action formalism. Right now im struggle to formulat what skeleton and 2-particle irreducible means, ...
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### Understanding from $S$-Matrix to Feynman-Rules in scalar QFT [closed]

I am learning QFT at the moment and the process from defining the S-Matrix to deriving the feynman rules is in my opinion pretty complicated, since there are many different things to pay attention to. ...
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### Resource recommendation for Renormalisation [duplicate]

I am learning renormalization by myself. I aim to understand one-loop calculations in $\phi^4$ theory in d dimensions and one-loop calculations in Quantum Electrodynamics. I have looked at Peskin and ...
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### Does choose-a-history work as a quantum interpretation?

This is a lay-reader level question about the interpretation problem in QM, from a QFT perspective. In his book QED, Feynman talks about how to calculate the probability density across a family of ...
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### Proof of Landau Conditions

I was reading this Quantum Field Theory book written by Claude Itzykson and Jean-Bernard Zuber. In section 6-3, page 304, the authors introduced analytic properties of Feynman integrals. Consider the ...
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### Decoupling of spurious states in leading order electron-positron annihilation

There are spurious states appearing in the canonical quantisation of the electromagnetic field, which do not represent physical states. In interacting theories, we exclude a spurious state of momentum ...
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### Feynman diagrams related to Hedin's equations and OEIS A286784

OEIS A286784 contains the lower triangular matrix 1; 1, 1; 2, 4, 1; 5, 15, 9, 1; 14, 56, 56, 16, 1; ... , with elements $T_{n,k}$ (initialized with $n=k=0$) which ...
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### From which interaction term does the self-energy diagram of $\phi^4$ theory come?

In 4D, let us start with the normal-ordered product of free neutral scalar fields $:\phi^4:$. Then, we can in fact write $$:\phi^4:=\sum_{i=0}^4 V_i$$ where each $V_i$ is an operator-valued ...
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### How can we expect the divergence of feynman diagram?

Suppose we have the Lagrangian in 3 dimensions: $$\mathcal{L} = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2-\frac{g_1}{4!}\phi^4-\frac{g_2}{6!}\phi^6$$ The superficial degree of ...
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### Electron–positron annihilation (Quantum electrodynamics)

I'm trying to learn a bit about quantum particles interactions and I've found something in Wikipedia that I find confusing. There are two different examples with different results about the same ...
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### Do we take care of the external momenta when finding the scalar 3-point function for $\phi^3$ theory?

The scalar 3-point function (1-loop correction) for $\phi^3$ theory could be found using the following diagram:  iV_3 = (-ig)^3\int\frac{d^4k}{(2\pi)^4}\frac{i^3}{[k^2-m^2][(k+p_1)^2-m^2][(k+p_1+...
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### Why there is no $u$ channel in fermion-antifermion scattering, but there is a $u$ term in $|M|^2$
I'm studying the Yukawa Lagrangian $g\phi\bar\psi\psi$: For ferimon-antifermion scattering, David Tong's QFT notes (p.121) have these Feynman diagrams: We can relabel the momenta and redraw the two ...
### Can a positive $W$ boson and negative $W$ boson exchange a lepton, and release a charged lepton antilepton pair or neutrino antineutrino pair?
Would it be possible for two passing $W$ bosons with opposing charge to either release a neutrino and become the corresponding charged lepton and charged antilepton, or release a charged lepton, and ...