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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Two identical output particles in decay and scattering process in quantum field theory

I am troubled for if we need to divide the factor of $2$ for two identical output states in decay and scattering process in quantum field theory. Consider Peskin and Schroeder's QFT book, on page 127, ...
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Tadpole diagram in one-loop QCD gluon self-energy renormalization

I am trying to study QCD renormalization at 1-loop order. So, when I take into account the gluon self-energy corrections, the book I am studying from says that there are three diagrams who contribute ...
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Contraction with external legs in $S$-matrix

If we consider following $S-$matrix element:$$\left\langle\mathbf{p}_1 \mathbf{k}_2|T\{\phi(x_1) \phi(x_2)\}| 0\right\rangle_0 $$ where $\phi$ denote Klein-Gordon field, and apply the convention in ...
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Definition of symmetry factor $p$ in Feynmans diagrams symmetry factor in Coleman's "Introduction to Many-Body Physics"

I'm trying to digest Coleman's 7.2.1 chapter about symmetry factors. Everything is clear up to point 4 where he introduces symmetry factor $p$ as the "dimension of the group of permutations under ...
4 votes
1 answer
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Ultraviolet Power Counting in the Four Photon Vertex

In the textbook Quantum Field Theory From Basics to Modern Topics, by François Gelis, the genuine ultraviolet degree of divergence for the four-photon vertex, as illustrated below, is found to be $-4$,...
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The two-loop $\beta$-function of the $\phi^4$ model

just recently I took an exam in QFT and the preamble was the following: We consider the $\phi^4$-model in $d = 4- \epsilon$ dimensions, defined by the action $$S = \int d^dx \left(\partial_{\mu}\phi(x)...
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Feynman's ammonia molecule

I have been reading Feynman's description of the quantum behaviour of an ammonia molecule. He assumes that the $\rm N$-atom is either pointing up or down as a two-states basis. He then says there is a ...
1 vote
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Help me figure out how to save the current in QFT

In studying quantum field theory, I encountered some difficulty. When considering the scattering diagram of the electron on the muon: Must be accomplished current saving $k_\mu j^\mu=0$ where $k=p^{(...
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3 votes
2 answers
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Reproduction of the explicit calculation of the Sunset diagram from the book Critical Properties of $\phi^4$ Theories (Kleinert)

The book starts with the equation \begin{equation} I(D) = \lambda^2 \int \frac{d^Dp_1}{(2\pi)^D}\frac{d^Dp_2}{(2\pi)^D} \frac{1}{\mathbf{p}_1^2 + m^2} \frac{1}{\mathbf{p}_2^2+m^2} \frac{1}{(\mathbf{p}...
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$\nu_e \bar{\nu_e} \rightarrow e^- e^+$ confusion

Interacting part of the $SU(2)_L$describing the Higgs and fermionic sector with one family $$\mathcal{L}= \bar{l}_Li\not Dl_L+\bar{e}_Ri\not\partial e_R+ \bar{\nu}_Ri\not\partial\nu_R - (y_{\nu}\bar{l}...
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Meaning of the bold line in Peskin and Schroeder's Feynman diagram

I'm studying chapter 6 of Peskin and Schroeder, on page 185, Peskin and Schroeder mysteriously used bold lines for the incoming and outgoing fermions $k$ and $k'$ but not $p$ or $p'$; The same bold ...
3 votes
1 answer
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Scalar derivative couplings: Effects on S-matrix and Feynman Rules

In Schwartz's field theory book ch. 7.4.2 he claims that interaction Lagrangians like $${\cal L}_{\rm int} = \lambda \phi_1(\partial_{\mu}\phi_2)(\partial_{\mu}\phi_3)\tag{7.101}$$ lead to the Feynman ...
2 votes
1 answer
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Converting Feynman Rules from in-out formalism to in-in formalism

For a standard set of Feynman rules (following in-out formalism) in momentum space, extracted from a generally given Lagrangian, is there a generic algorithm for converting them into the Feynman rules ...
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Attractiveness of Coulomb potential from Peskin-Schroeder textbook

On page 125 chapter 4.8 of Peskin & Schroeder "An Introduction To Quantum Field Theory" there's a sort of argument that should prove that in the non-relativistic limit of QED like ...
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Mass renormalization counterterm in Wilsonian effective action diagram

this is my first post on stack exchange so please pardon me any mistakes or bad format. My question is about counterterms and the Wilson effective action. We started in Euclidean spacetime from $$\int ...
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Lagrangian-Feynman diagram renormalization equation

Quick question but I read this form and on the answer, it showed equations $$ \mathcal{L}_0(g_i)\;\to\;\boxed{\mathcal{F}_\Lambda}\;\to\;f_j(g_i,\Lambda)\,, $$ and $$ \mathcal{L}_1(g_1,\ldots g_{n+1}) ...
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Why right-handed neutrino?

Interacting part of the $SU(2)_L$describing the Higgs and fermionic sector with one family $$\mathcal{L}= \bar{l}_Li\not Dl_L+\bar{e}_Ri\not\partial l_L+ \bar{\nu}_Ri\not\partial\nu_R - (y_{\nu}\bar{l}...
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how can the virtual fermionic lines be vertical in kaon mixing feynman diagram?

how can the virtual fermionic lines be vertical in kaon mixing Feynman box diagram (or in general)? Wuouldn't this mean that they travel a distance $\neq 0$ in 0 time?
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1 answer
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Feynman diagram with different particles

I'm studying Peskin and Schroeder chapter 5. At the beginning of section 5.1, the book tries to compute S matrix of $e^+e^-\rightarrow \mu^+\mu^-$. Using the Feynman from section 4.8, we can draw a ...
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Calculating the superficial degree of divergence for arbitrary nPIR diagram

In Weinberg QFT Vol 1 Ch. 12, he only calculates the superficial degree of divergence $D$ for 1PIR diagrams. The formula is given by \begin{equation} D=4-\sum_f E_f(s_f+1)-\sum_i N_i \Delta_i \end{...
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Feynman rules after a Hubbard-Stratanovich transformation, i.e. for a field with no kinetic term

I am trying to calculate the beta function of the 2D Gross-Neveu model after performing a Hubbard-Stratanovich transformation. Of course, you can calculate it without this transformation, but I am ...
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Feynman Two Loop Integrals

Is there any reference suitable for a beginner that you recommend for learning two loop integrals evaluation by hand ( and/or some package) that you know of?
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The distinction between real and virtual particles

I will take the simple case of a spin-0 field: $$W(J)=-\iint d^4xd^4y J(x)D(x-y)J(y)$$ which in the Fourier transform becomes: $$W(J) = -\int d^4 p J(p)^* \frac{1}{p^2-m^2+i\epsilon} J(p)$$ what I ...
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How can I see mathematically with Feynman rules of QED that same charges repel and opposite charges attract?

I'm trying to 'prove' that electrons repel each other and electrons-positrons attract each other, but I'm not sure what I should be looking at. My guess is that there should be a different sign when ...
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1 answer
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Scalar QED - pair annihilation into photon cross section

I just spent the last three days trying to compute the cross section of a process of pair annihilation of complex scalars to a pair of photon in scalar QED. For some reason I don't seem to be able to ...
1 vote
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How does Feynman justify using this propagator expansion on the Dirac equation?

I'm slowly wading through Feynman's series of three papers from 1948-49 (Space-Time Approach to Non-Rel QM, Theory of Positrons, Space-Time Approach to QED). I think they're brilliant and they are ...
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The presence of $\zeta^{\mu}(k)$ in the Ward-Takahashi identities in QED

On page 132 of Timo Weigand's QFT notes we introduce the Ward-Takahashi identity for QED, this is the statement that: $$k^{\mu}\mathcal M_{\mu}(k)=0 \tag{5.35},$$ with $$\mathcal M(k)=\zeta^{\mu}(k)\...
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1 answer
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Why exact propagators as external lines in Feynman diagrams are assigned a factor of $1$ in perturbation theory in all orders?

I'm reading Srednicki's QFT and I've met a problem in a footnote of section 19. In calculating the Feynman diagrams to all perturbative orders, we only calculate tree-level diagrams but use exact ...
2 votes
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Amplitude of fermion decay with Majorana mass insertion

Consider the following Lagrangian, $$ L \supset \frac{1}{2} m \overline{\psi}\psi^C + g \phi\, \overline{\chi}\,P_R\,\psi + \rm{h.c.} $$ where $\psi$ is a heavy fermion with a Majorana mass $m$, $\phi$...
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On energy conservation and time-ordered interaction diagrams

I've found the following lectures given by professor Mark Thomson (here's his particle physics web page); in the third one, Interaction by particle exchange and QED, it's stated that time-ordered QM ...
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1 vote
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Charge Conjugation

For my calculations I need to know how charge conjugation acts on the Spin 3/2 propagator. The charge conjugation operator $C$ is calculated as $C= i\gamma^2\gamma^0$. The Spin 3/2 propagator is $$ S_{...
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1 answer
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How is it justified to use two different coupling constants for tree-level diagrams and diverging diagrams?

For tree-level amplitude, we're using the finite constant determine using experiments ($\lambda _R$) For diverging amplitudes, we're using a different constant: $\lambda _R+ C\ln \frac{\Lambda ^2}{s_0}...
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Relation between Feynman diagrams and the effective action [duplicate]

I have learned that the effective action can be obtained from legendre transforming the generating function $$W(J) = \ln(Z(J)),$$ which corresponds to connected graphs. However I don't quite get an ...
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Are self-loop diagrams zero if $L_\text{int}$ has a derivative term?

I was looking at the theory with interaction Lagrangian $L_\text{int}=\phi^3 \cdot \partial_{\mu}\phi$. I was computing the following self-loop diagram \begin{equation} \langle \phi_x \phi_z^3 \cdot \...
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On physical interpretation of Mandelstam variables

The accepted answer to this post gives a nice physical explanation of the Mandelstam variables. The only problem is that each variable seems to make sense only within a specific channel. Take the $t$ ...
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3 votes
1 answer
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How - if at all - does the integral $\int_{0}^{1} \Big{(} \frac{\ln(1-x)}{x} \Big{)}^{n} dx $ arise in Feynman diagrams?

In the following table by A. Devoto and D. W. Duke, a number of logarithmic integrals are listed that - according to the authors - help with Feynman diagram calculations. In particular, integral (3.6....
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Sources to find Feynman diagrams of scalar field

I am currently doing a project i.e. collection of Tree level and 1-loop Feynman diagrams corresponding to various scalar fields and very soon I got out of sources. I am very much new to QFT. Can any ...
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Explicit calculation of the effective action for $\phi^4$ by a Legendre-transformation

Let's say my generating functional for the connected moments is given by \begin{align} W[J]&=\underbrace { -\frac { 1 }{ 2N } \ln { ( } Na) }_{ { ring } } +\underbrace { \frac { 1 }{ N^{ 2 } } \...
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1 vote
1 answer
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Minus sign in Feynman's The reason for antiparticles

I was going through Feynman's lecture on "The reason for antiparticles", which can be found here, and I got a little confused early on. His statement of Eq. 3 seems clear to me, from which ...
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3 votes
1 answer
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Gauge-invariant vertex structure for $h\to\gamma\gamma$ via fermion loop

I am struggling (a bit) with the following diagram for scalar Higgs to two photons. $h\to\gamma\gamma$" /> If I put $q_\mu$ on-shell (or at the very least if I put both $q_\mu$ and $q'_\nu$ on-shell), ...
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Renormalization in $\phi^3 + \phi^4$ theory in $D=4$

While reading notes on renormalization, specifically one-loop renormalization of $\phi^4 +\phi^3$ theory (Real Scalar Field) in $D=4$, In the section about corrections to coupling constants. For the ...
1 vote
1 answer
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Why are positrons traveling backward in time in Feynman diagrams?

We draw the positron as if it's traveling backward in time. Why? The momentum of the positron is drawn opposite to the time-direction of the diagram. I don't see this having any effect on the ...
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2 votes
1 answer
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Why is it that the box loop diagrams do not contribute to the $\phi\phi\rightarrow \phi\phi$ one-loop beta-function in a $\phi^3$ theory?

I have read at a few places that the box diagrams do not contribute as they are UV finite, but why would a UV finite diagram not contribute to the beta function? Or is it something else I am missing ...
3 votes
1 answer
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$\Gamma^{1PI}$ contribution to the effective action $\Gamma$

So I am currently taking a class on advanced quantum field theory, and I came across something that I don't understand. I have been thinking about it for quite some time and I cannot get my head ...
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3 votes
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Correct way to expand the generating functional

Consider the following self-interacting real scalar field theory $$ \mathcal{L} = \frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi) - \frac{1}{2}m^2\phi^2 - \frac{\lambda}{4!}\phi^4 $$ with $m^2 > 0$ ...
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2 votes
1 answer
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One-loop triangle integral with equal masses

This is a question about the explicit form for an integral that is very common in QFT. $$I_3(p,p';\,m,d)\equiv \int \frac{d^d k}{(2\pi)^d} \frac{1}{\left(k^2+m^2\right)\left((k+p)^2+m^2\right)\left((...
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One-loop correction $\phi^4$ theory

Consider the following one-loop diagram: The corresponding expression in momentum space is: \begin{equation} (-i\lambda)\int \dfrac{i}{k^2-m^2+i\epsilon}\frac{d^4k}{(2\pi)^{2}} \end{equation} (...
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Do I have to take the trace over gamma matrices in Yukawa vertex correction?

Given the Yukawa coupling $\mathcal{L}_{\text{int}}=g\phi\bar{\psi}\psi$, if I want to compute the correction to one loop to the vertex, I would write something like this $$\Lambda\sim g\int\frac{d^...
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What is the difference between vertex and current in Feynman diagram?

As the title suggested what is the difference between them? For example, $u$ quark turning to $d$ quark via $W$ boson, and the vertex should be written as $$\bar{u}\gamma^{\mu}(1-\gamma^5)d$$, well ...
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Elastic quark-quark scattering

I try to write expression for qq->qq proccess with double gluon exchange I figured out the denominator, but i cant understand how to write numerator. My thoughts are: \begin{equation} numerator = g^...

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