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-...
- 205
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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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Combinatorics for Feynman Diagrams [closed]
When one wants to calculate the two-point-function for an electronic system with Coulomb-interactions in quantum many body systems with the path-integral-formalism
$$
\mathscr{G}_{ \alpha , \alpha^{ \...
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Can someone explain this Feynman Diagram in the picture?
I don’t understand this diagram at all, and what is the meaning of the $g$?
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Summing graphs in the partition function (statistical physics)
I am looking at Tong's lecture notes on statistical physics, and I wanted to understand a step in his cluster expansion better.
The goal here is to calculate the partition function in the canonical ...
- 189
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The proper self-energy diagrams for the Anderson model
According to Fetter's book, the Feynman diagrams contribute to the proper self-energy are:
where the first and second orders here refer to the perturbation expansion of the interacting Green's ...
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Order by order renormalization
This post is a little bit related with my last post, where I don't totally understand one point. I think it's better to write a new post specialized for this point.
For a renormalized $\phi^4$ theory, ...
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Peskin & Schroeder Introduction to Quantum Field Theory, two-loop renormalization example
In Peskin & Schroeder's An Introduction to Quantum Field Theory, section 10.5, page 338, the book gives a two-loop renormalization example (in scalar $\phi^4$ theory).
Before we start the two-...
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Numerators in LoopTools
I want to calculate the diagram
$$ \int \text{d}^D q \frac{q_\mu q_\nu q_\rho q_\eta}{(q^2-m_1^2)((q_1+p_1)^2-m_2^2)((q_1+p_1+p_2)^2-m_3^2)((q_1+p_1+p_2+p_3)^2-m_4^2)((q_1+p_1+p_2+p_3+p_4)^2-m_5^2)} $$...
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Calculation of one-loop diagram in $\phi^4$ theory
In Folland's book Quantum Field Theory, page 207, he gives the value of the amputated one-loop $\phi^4$ diagram as
$$I(p) = \frac{(-i\lambda)^2}{2} \int \frac{-i}{-q^2 + m^2 - i\epsilon} \cdot \frac{-...
- 1,902
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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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Feynman rules for Majorana fermions?
I want to deduce the Feynman rules for neutrino magnetic moment, and there are Dirac and Majorana terms for this
$$\mathcal{L}_D=\mu_{ij}\bar{\nu}_{iL}\sigma_{\alpha\beta}\ \nu_{jR}F^{\alpha\beta}$$
$$...
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What numerical methods can be used to verify the accuracy of Feynman diagram results?
Recently, I have been attempting to replicate the Feynman diagram calculation which was featured in an article here.
\begin{align}
&C_{x y x y}^{1, e}(i \Omega)= -(1-\delta) r_0^{-\delta} 2^{4+\...
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Creation and destruction of particles in the Path integral
Reading Zee's QFT book he defines the interacting partition function as follows
$$Z(J,\lambda)=\int\mathcal{D}\varphi \exp{\left(i\int d^4x \left[\frac{1}{2}((\partial\varphi)^2-m^2\phi^2)-\frac{\...
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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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Why doesn't this diagram appear in the partition function in zero-dimensional QFT?
For the zero-dimensional QFT with action
$$S(\phi)=\frac{\alpha}{2}\phi^2+\frac{\lambda}{4!}\phi^4-J\phi,\tag{1}$$
we can perturbatively expand the partition function as
$$Z_\lambda(J)=\int_{-\infty}^{...
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How to compute unpolarized cross section for $e^−+\gamma \to e^−+\pi$
I need some help with this calculation. I have already made a few attempts but, even applying Feynman's rules for QED on the first vertex and for Yukawa interaction on the second one, I cannot figure ...
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Prefactor to amplitude for massless fermions/massive bosons
I was reviewing some of my old notes and found this formula for a matrix elements between two states:
$$
<f|S|i>= \delta_{fi} + [(2\pi)^4 \delta^4(P_f - P_i) \prod_{ext. fermion}\left(\frac{m}{...
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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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Why do we have this divergent graph as odd diagrams are excluded?
I got a follow-up question to my earlier post.
Suppose we have the pseudoscalar Yukawa Lagrangian:
$$
L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\bar\psi(i\not\partial-m)\psi-...
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How soft photons carry away energy
While studying the infrared traces, I came across the following Feynman diagram:
This diagram shows the braking radiation and the radiation correction of a soft photon. There are three vertices in ...
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Why do we Wick rotate before regularizing Feynman diagrams?
In Folland's Quantum Field Theory he mentions that we can apply Feynman's formula (Feynman parameterization) to either the Wick rotated integrals or the non-Wick rotated integrals corresponding to ...
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How to understand this diagram, and is it relevant to the renormalizability of a theory?
I'm having trouble understanding this diagram from my lecture note:
Each grey-shaded circle represents the diagrams for the two-point function $D(k)$. In equation, the diagram reads$$ \bar G_n(k_1,......
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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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External momenta in renormalizing pseudoscalar Yukawa theory
This is a follow-up question to my earlier post here:
Now suppose we have the pseudoscalar Yukawa Lagrangian:
$$
L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\bar\psi(i\not\...
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Should the sign of Feynman rule factors be the same as the sign in the Lagrangian?
Suppose I have this Lagrangian
$$
L = \frac{1}{2}\partial^\mu\phi\partial_\mu\phi - \frac{1}{2}m^2\phi^2-\frac{g_3}{3!}\phi^3
$$
One of the Feynman rules would be associating a factor $(-ig_3)$ to ...
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Does the 1-loop correction for $g\bar\psi\psi$ term leads to the counterterms for additional terms in the Lagrangian?
I have the Lagrangian in 4 dimensions:
$$
L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\sum_{i =1,2}\bar\psi_i(i\not\partial-m)\psi_i-g\phi\bar\psi_i\psi_i.
$$
Assuming there ...
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Why is this rearrangement of factors in the Compton Scattering matrix element valid?
I've been trying to follow through this derivation of the total squared matrix element for Compton scattering. We have two first-order diagrams:
Using Feynman rules, the matrix elements for each ...
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How do we determine momentum when going from position space to momentum space in Feynman diagrams?
I have read chapter 4 in Peskin & Schroeder on interacting fields and Feynman diagrams. I believe I have some fundamental misunderstanding, so I have outlined what I know so far below and included ...
- 1,902
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Sub-series of a perturbation series and summation of infinite diagrams
In many-body perturbation theory like in, Altland and Simons: Condensed matter field theory, 2nd edition, we express a correlation function in terms in an perturbation series. My understanding is ...
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Deriving the charged pion decay matrix element
From M Schwarz's QFT (p 570), Goldstone's theorem indicates that pions are created from the vacuum by the chiral ${\rm SU}(2)$ current $J_\mu^{5a}$,
$$
\langle
\Omega|
J_\mu^{5a}(x)|\pi^b(p)
\rangle
=...
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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 ...
- 1,305
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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 ...
