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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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377 views

Cutoff-Scheme Renormalization and Order of Integration in QFT

The following is the result of Fubini's Theorem, describing when you can replace a double integral with an iterated integral safely: For a set $X \times Y \subset \mathbb{R}^2$, if $\iint |f(x,y)| d(...
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gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
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In QED/Yang Mills, why do fermions contribute 4 times as much as scalars to vacuum polarization?

Consider a Yang-Mills theory in $4D$ over a gauge group $G$ $$ \mathcal{L} = - \frac{1}{4} F^{a\mu\nu}F_{\mu\nu}^a + \bar \psi i D_\mu \gamma^\mu \psi + (D_\mu \phi)^\dagger D^\mu \phi $$ where $\...
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Ward identity for 'general' operator and current diagrams

This is actually about two related doubts and I hope is appropriate for a single question (if not, I will happily divide it). So, my problems are related to the analysis and calculation of chiral ...
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243 views

Questions about the equivalent forms of Wick's theorem?

NOTE: The problems have been editing with more details. I have met Wick's theorem first in this book fundamentals of many-body physics when talking about the perturbation expansion of zero ...
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324 views

What is the effective (quantum) lagrangian of a fermion field for fixed electromagnetic field?

... or, put it another way, what are the loop corrections to the dirac equation in the presence of a fixed (external) electromagnetic field?. Background Let $\mathcal L=\frac{1}{2}(\partial\phi^2+m^...
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536 views

An use of the Schwinger-Dyson equation

I was confused as to how the equation 10 on page 7 or equation 21 on page 8 of this paper http://arxiv.org/abs/1211.1866 was derived. Can someone explain from where does this come and what do the "...
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127 views

Supergraphs and their Feynman rules

I am reading Ideas and Methods of Supersymmetry and Supergravity, and have two confusions on using supergraphs, and applying the Feynman rules. As an example of the conceptual issue I have, a result ...
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126 views

Tadpoles in sigma models

In some QFTs, the tadpoles are not taken into account, since they vanish due to certain symmetries of the theory. Peskin and Schröder address this issue in QED around Equation (10.5) of their book; ...
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446 views

Why do tadpoles contribute to amplitudes?

In some quantum field theories tadpoles of the form                           &...
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265 views

Variations of S-matrix functional and Feynman diagrams in Weinberg QFT

Weinberg on p. 287 of his QFT vol. 1 introduces the extended interaction operator: $$ \tag 1 \hat{V}(t) \to \hat{V}(t) + \sum_{a}\int d^{3}\mathbf x \hat{o}_{a}(\mathbf x ,t)\varepsilon_{a}(x). $$ ...
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Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: $S[\phi,\sigma]=\int{d^4x[-\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2-\frac{1}{2}M^2\sigma^2-\...
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Understanding the intermediate field method for the $\phi^4$ interaction

In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to ...
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How to calculate $n$-point functions of interacting fields in curved spacetime (Schwarzschild metric)?

How to renormalize quantum field theory in curved spacetime? (or in Schwarzschild spacetime?)  I want to calculate n-point functions $$<0|Tφ(x_1)...φ(x_n)|0>$$ in massless $φ^4$ theory in ...
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1answer
352 views

Massive versus Massless $\phi^4$ Sunset Diagram - does $\frac{1}{\epsilon^2}$ term vanish for $m=0$?

In a real scalar massive $\phi^4$-interacting theory consider the amputated sunset diagram. This is the integral out of Kleinert and Schulte-Frohlinde Critical Properties of $\phi^4$-Theories: The ...
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Feynman rules for this perturbative expansion in Grassmann variables

I'm given the integral $$ Z[w] = \frac{1}{ (2 \pi)^{n/2}} \int d^n x \prod_{i=1}^n d \overline{\theta}_i d \theta_i \exp \left( - \overline{\theta}_i \partial_j w_i (x) \theta_j - \frac{1}{2} w_i(x) ...
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334 views

How can I see where this formula for a general vertex factor comes from?

I have been reading Srednicki from the beginning and doing all the exercises, and I hit a big roadblock at Q10.4, as I can't seem to figure out what Srednicki is doing in his solution. Luckily, I ...
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492 views

Fermion self-energy

I try to calculate the mass matrix for a massless fermion mediated by a loop of massless (right handed) neutrino and a scalar like the next diagram The amplitude is given by: $$ i M = \bar{u}_{s_i}(...
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671 views

Srednicki's QFT: Feynman Rules and Feynman Diagrams

I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. The path integral for the ...
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118 views

What is the recursive relation for three-particle Green's functions?

In condensed matter physics, one often choose to study the many-body Green's functions (GF) with the diagram (perturbation) expansion technique. In what follows only two-body interaction is concerned. ...
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The Ward identity for EM amplitude with massive vector boson

Let's have theory of massive vector boson interacting with EM field: $$ L = |D_{\mu}W_{\nu} - D_{\nu}W_{\mu}|^{2} + m^{2}|W|^{2}, \quad D_{\mu} = \partial_{\mu} - ieA_{\mu}. $$ The question: how to ...
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225 views

S-Matrix Generating Functional (Problem 4.1 in Weinberg)

I'm currently working through Weinberg's QFT book, but I'm somewhat stuck at problem 4.1, which states: Define generating functionals for the S-matrix and its connected part: \begin{equation} F[\...
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398 views

Symmetry factor of tree diagram

In Mark Srednicki's Quantum field theory(page 89) it says This is a general result for tree diagrams (those with no closed loops): once the sources have been stripped off and the endpoints labeled,...
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538 views

Why do we use functional integration in QFT?

Recently I learned functional integral's formalism in quantum field theory. I have realized that I don't understand why exactly do we introduce it. We have the expression for $S$-matrix, then we may ...
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Can $\langle\Omega|f|\Omega \rangle$ always be reduced to $\langle0|f|0\rangle$?

I've not come across any expression involving $\langle\Omega|f|\Omega\rangle$ in Srednicki's QFT book (please correct me if these exist there). On the other hand, they are abound in Chapter 7 of ...
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382 views

Vertex for quartic interaction of complex scalar multiplet

Since I'm new to QFT and I tend to do a lot of errors during calculations, I would like you to tell me if I got the four-point vertex of the quartic interaction with a multiplet of complex scalar ...
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Helicity dependence in loop diagrams

I am trying to evaluate a diagram that looks like The middle of the diagram is a fermion loop. I know that the coupling between the $Z^0$ and fermions depends on the fermions' helicities, so it ...
4
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1answer
336 views

Relation between symmetry factors

In $\phi^3$ theory, the generating functional for interacting field theory is given by: $$ Z_1(J) = \sum_{V=0}^{\infty} \frac{1}{V!} \Big[ \frac{iZ_g g}{6} \int \Big( \frac{1}{i}\frac{\delta}{\delta J}...
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1answer
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Feynman Diagram for Bragg Equation

Did Feynman ever derive the Bragg equation as a particle representation using Feynman diagrams? And where is it available? I spoke to Freeman Dyson and he couldn't recall.
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An equivalent computation of a Feynman diagram

A typical second-order diagram for the self-energy gives integrals such as: $$\int \int d \omega^\prime \omega^{\prime \prime} g(\omega-\omega^{\prime})g(\omega^{\prime \prime})g(\omega^{\prime}+\...
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Scalar electrodynamics “seagull” vertex factor

By expanding the covariant derivative of the Scalar QED lagrangian one gets the following term, sometimes called "seagull" vertex. $$\mathcal{L}_{seagull} = -q^2A_\mu A ^\mu \phi^\dagger \phi$$ Most ...
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1answer
156 views

Combinatorics geometric series two-point function

In this answer Proof of geometric series two-point function it is said: Now what about the coefficients in front of each Feynman diagram? Due to the combinatorics/factorization involved it ...
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159 views

Feynman diagrams included in Hartree-Fock approximation

Given a hamiltonian, I compute the Hartree-Fock self-energy. Let's say I now compute the second order self-energy with diagrams. Some of them are just like the Hartree or Fock diagrams of first order, ...
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Infrared divergencies in Yang-Mills theory

I'm trying to better understand the nature of infrared divergencies in YM theory; for now, I'm only interested in soft divergences. The usual explanation one is given about the origin of IR ...
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201 views

Is Wick rotation of loop integrals legitimate?

In Feynman diagram calculations, we seem to invariably Euclideanise loop integrals in order to exploit the resulting spherical symmetry. This Wick rotation is simply a deformation of the contour; ...
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Identifying diagrams for optical processes

I was reading some papers on the study of the optical properties of some metals and came upon these conference proceedings by Hopfield from 1972. They are on the study of the infrared properties of ...
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405 views

S-matrix for $\phi^3$ theory

In the book Quantum Field Theory for the gifted amateur by Tom Lancaster & Stephen J Blunden, in the chapter about expanding the S matrix they give an example using the $\phi^4$ Langrangian, $$ \...
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Why are there no linearly divergent terms in the sunset diagram?

Consider the following 2-loop 1PI diagram for the $\lambda \phi^4$ theory. This is given by the following integral: $$-i\ \Sigma(p^2) = \frac{(i\lambda_0)^2}{\#} \int\frac{\mathrm d^4s}{(2\pi)^4}\...
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Appending a Noether current to a Feynman rule

Background Typically in QFT one derives the Feynman rules by differentiating certain terms in the Lagrangian w.r.t the relevant fields. So for instance if our term is $\mathscr{L} =\phi_1\phi_2\phi_{\...
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2answers
263 views

Pauli- Villars regularization in the Electron Vertex Function: Evaluation

I'm studying one loop contribution for electron vertex function form Peskin and Schroeder's book " An introduction to quantum field theory " Section: 6.3. I have some troubles with Pauli- Villars ...
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991 views

Tree-Level Feynman Diagrams for the Phi-Cubed Theory

The following question is from the discussion on Scattering Amplitudes and Feynman Diagrams (Chapter 10) in Srednicki's QFT. For the connected correlation function, we have for the $\phi^3$ theory: ...
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Two Loop QED Feynman Diagram

I'm trying to find the momentum space integral representation of the below Feynman Diagram, but am having troubles with the fact that there are two loops within the system. The main question I have ...
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how to construct self-energie diagrams

I am working on self-energie and feynmann diagrams. they are not very easy to get but i think i am starting to understand how it works but of course i am not realy sure.and before going any further i ...
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1answer
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What is a Witten diagram?

Recently I heard the terminology of Witten diagram. Studying QFT, I frequently see Feynman diagrams and use them to compute scattering amplitudes, one-loop corrections and so on. In string theory ...
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$\phi^4$ theory two-loop contributions

Wherever I see calculations of two-loop contributions to the $\phi^4$ propagator (such as Peskin, page 328, on the bottom), only the sunset diagram (aka the Saturn diagram) is considered, but not, say,...
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251 views

Perturbation theory : quadratic external field

I'm trying to derive the explicit form of S-matrix of an interaction Hamiltonian $$H' = \frac{1}{2} \lambda \left[ \int d^3 x \rho({\vec x}) \phi({\vec x}, t)\right]^2\tag{1}$$ Even though the ...
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Why only fully connected diagrams contribute to T matrix

In Peskin's introduction to QFT, he wrote: only fully connected diagrams, in which all external lines are connected to each other, contribute to the T matrix. I don't understand this statement. ...
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236 views

What is the phase space for outgoing photons?

For a scattering process for which $n$ fermions are scattered, (by some conventions) the cross section acquires a phase space factor of: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$ In ...
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235 views

Feynman Toy Model Constraints on Number of Each Kind of External Lines

(From my homework) In our toy model we have three kinds of spinless particles: $A$, $B$, and $C$. The primitive vertex of decay/interaction is shown below: My actual problem statement says: "...
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Scattering theory on Schrodinger and Feynman languages

Recently I heard that both of "languages" of scattering theory (formal solution by method of classical scattering theory and its reworking by Feynman with his rules) predict virtual particles. But for ...