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0
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0answers
104 views

Mass term in field Lagrangian

In the Klein-Gordon or in the Dirac Lagrangian density, the mass term is quadratic in the field. The other way around, I have heard a quadratic term in a general Lagrangian density be referred to as a ...
2
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1answer
146 views

Feynman diagrams and gluon collisions/interactions?

We have been given this question which essentially asks us to draw the lowest order Feynman diagrams for various processes. One of them is: $$ g + g \rightarrow \bar{t}+t $$ Now, I am not an expert ...
0
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0answers
131 views

Feynman Diagrams Integral Calculation

Are there any easy tricks to calculate integrals of the form: $$\int d^4x \ e^{ikx} \dfrac{1}{x^2} \ \ (\text{ans:} \ i\dfrac{4\pi^4}{k^2}) \ \ \text{and} \ \ \int d^4x \ \mu^2 \dfrac{\ln x^2}{...
0
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0answers
75 views

How are tree-level calculations related to the classical theory?

I've read the answers (and linked notes) to another question (Tree level QFT and classical fields/particles) and I understand them. They seem to explain how to organise a perturbative calculation of ...
1
vote
0answers
77 views

How do I derive Feynman rules for vectors involving derivatives?

Suppose I have a term in the Lagrangian: $$\cal{L} \equiv (\partial_\mu B^+_\nu) B^{-\mu} A^\nu $$, where $B^\pm$ are charged massive vector particles and $A$ is photon. Now, how can we derive the ...
5
votes
1answer
254 views

Scattering Amplitudes from Feynman Diagrams (Spinor Helicity Formalism)

$\require{cancel}$ I am trying to do an exercise from Scattering Amplitudes By Elvang (Exercise 2.9) which states: Show that $A_5(f^-\bar{f}^-\phi\phi\phi) = g^3\frac{[12][34]^2}{[13][14][23][24]} ...
1
vote
1answer
236 views

Feynman Diagrams for Yukawa Theory

I am trying to draw the Feynman diagram for the following scattering amplitude (f a fermion) $$ i\mathcal{M}(f\overline{f}\phi\phi\phi) $$ Given the following interaction term in the Lagrangian: $$ \...
1
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1answer
114 views

Meaning of angles on Feynman diagram

In physics class, I am currently studying Feynman diagrams. We are taught the basics like conservation of charge and the direction of time but the examples in my book all seem to follow specific paths ...
1
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0answers
71 views

Correspondence between variational method and Feynman diagrams

There are two ways to look at the Hartree or Hartree-Fock equations. One method relies on the variational method for a particular type of the probe function and the second one originates from ...
2
votes
1answer
115 views

complicated QCD Color factor formula?

I was doing higher order calculations for purely gluonic system and came across complicated color factors like the product of six structure constants product $f_{a_1a_2a_3}f_{a_4a_2a_7}f_{a_7a_8a_1}f_{...
2
votes
1answer
140 views

What are skeleton diagrams and what is their use in qft and many-body physics?

How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, ...
1
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0answers
80 views

The second order scalar quartic field theory Feynman diagrams

I'm trying to find the second order Feynman diagrams for the scattering of a scalar phion, described by the Lagrangian $$ L = L_0 + L_I \\ L_0 = \frac{1}{2}[\partial_{\mu} \phi(x)]^2 - \frac{1}{2}m^2 ...
4
votes
2answers
892 views

What is going on in the photon-photon scattering Feynman diagram?

I understand the basic concepts of a Feynman diagram, but I don't get what is going on here. I have named the photons ABCD and the fermions 1234 for clarity. I'm going to assume that the vertical ...
0
votes
0answers
52 views

Cuts of a Feynman diagram and the massless limit

Consider a $j$ point all massive leg one loop polygonal Feynman diagram $P$ representing some scattering process cut on a particular mass channel $s_i$. Invoking the relevant Feynman rules and ...
8
votes
1answer
118 views

Why is a vertex a derivative of the propagator?

Where can I find the proof to this nice trick: if the momentum $q$ is small, the vertex is the derivative with respect to the mass of a propagator times a factor $(-m/v)$ like in the picture:
1
vote
0answers
98 views

Is there any difference in mixing and oscillation of neutral mesons?

I have often read about neutral Kaon oscillation or neutral B meson mixing. Both are described by the similar box diagrams. So I want to know if we can say neutral kaon mixing and D meson oscillation.
2
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0answers
81 views

Second order pole in Feynman diagrams

Hi, I am calculating density-density correlation function for a homogeneous electron gas. The Green's function for one of three first order connected diagrams(see attached figure) is, $$ \textit{...
4
votes
2answers
76 views

Multiplying propagators

The amplitude for a particle going from $x$ to $y$ is $G(x,y)$. So why isn't the amplitude for going $x$ to $y$ to $z$ $$ G(x,z) \neq \int G(x,y)G(y,z) dy^4 $$ but instead $$ G(x,z) = \int G(x-y)...
0
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0answers
33 views

Is one of the matrix elements in the optical theorem complex conjugated or not?

The standard form of the optical theorem for amplitudes (Edit: in D-dimensional space-time) looks like this: \begin{align*} -i& (\mathcal{M}(in \rightarrow out)-\mathcal{M}^*(out\rightarrow in))\\ ...
1
vote
1answer
50 views

Feynman rule for current-current operators

I wanted to know what is the Feynman rules for current-current vertex like this one: $$ {\cal{ L}} = G^\prime_F \hspace{2mm} \bar{d} \gamma^\mu (1-\gamma^5) u\hspace{3mm} \bar{s}\gamma_\mu (1-\gamma^...
1
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0answers
49 views

Normalising a massive propagator?

If you take a propagator Greens function for a massless photon from the origin as $$G(0,x) = \frac{1}{x^2-t^2 +i \varepsilon}$$ then the normalisation factor at time t is: $$ N = \int |G(0,x)|^2 d^...
2
votes
1answer
148 views

Feynman diagrams vs Feynman integrals?

It is well-known how one can translate a (physical) Feynman diagram into integrals of kind: $$I(p_1, \dots, p_n) = \idotsint \prod_{l=1}^{L} \frac{d^D k_l}{(2\pi)^D} \frac{\text{scalar products}}{\...
1
vote
0answers
53 views

Dependence of scattering amplitudes on Mandelstam variables

It is well-known that scattering amplitudes in QFT are tensors, hence e.g. scalar amplitudes /written in momentum space/ depend only on the Mandelstam variables of the external momenta, involved in ...
1
vote
1answer
80 views

Charge of $W$-bosons in Feynman diagrams

When looking at Feynman diagrams of particle decays, how would I be able to find out the charges of the $W$-bosons involved in the decay?
2
votes
1answer
137 views

How was this one probability amplitude derived by Mattuck?

I'm reading A Guide to Feynman Diagrams in the Many-Body Problem by Richard D. Mattuck (2nd edition). You can look at the relevant pages here. On page 45, he presents a formula for $D_t c_p(t)$. ...
3
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0answers
204 views

One-particle scattering: LSZ vs Feynman [duplicate]

This question is about Klein-Gordon theory (the field is hermitian). If I calculate the amplitude for the process $\phi\to\phi$, I get two different results depending on whether I use Feynman rules ...
7
votes
3answers
282 views

Contradictory result for scalar-field propagator from Feynman rules and LSZ formula

I am trying to learn how to calculate scattering amplitudes in a Klein-Gordon theory. I am getting stuck with the simplest of the examples: $\phi\to\phi$ in a free scalar-field theory. If I calculate ...
1
vote
1answer
145 views

What is the defintion of a current-current diagram?

Right now I am facing some Feynman diagram calculations and in the instructions I am reading the phrase current-current diagram appears quite often so I wanted to know: What is the definition of a ...
1
vote
0answers
31 views

Is there a useful way to represent the optical theorem in the parametric representation?

The usual way to represent the optical theorem for Feynman diagrams is through the Cutkosky rules. The proof of these rules works by considering the momentum representation and performing the iterated ...
6
votes
2answers
75 views

How are quadruple gluon vertices related to $SU(2)$ and $SU(3)$?

I once read that the non-commutativity of the Lie Groups $SU(2)$ and $SU(3)$ is the reason that the weak and strong interactions have Feynman diagrams with quadruple vertices, where four gauge bosons ...
1
vote
2answers
96 views

Does the connected Green's function's decomposition into 1PI-s have connected contributions, or can it be written exclusively using 1PI-s?

While reading this article by Abbot on the background field method, in Fig 5. on page 38 (page 6 in the pdf file), we can see the relation between connected contributions to the two point function and ...
3
votes
1answer
186 views

Two math methods apply the same loop integral lead different results! Why?

I tried to adopt the cut-off regulator to calculate a simple one-loop Feynman diagram in $\phi^4$-theory with two different math tricks. But in the end, I got two different results and was wondering ...
1
vote
0answers
174 views

How do the renormalization enter the actual amplitude calculation in QFT?

I have studied QFT from Peskin and Schroeder and from a few other books and lectures and I think I understand the procedure of renormalizing various parameters in the Lagrangian like mass, coupling ...
1
vote
0answers
81 views

Clarification on Use of Counterterms in Renormalized Perturbation Theory

In renormalized perturbation theory, it's unclear to me how exactly we add the necessary counter-terms. Do we: Draw all possible diagrams, including the diagrams of the counter-terms to some order ...
2
votes
0answers
374 views

$\phi^4$ 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,...
1
vote
1answer
160 views

Compton Scattering Feynman diagram integral expression

I'm trying to write down the integral expression according to the feynman-rules for this Diagram of an electron with compton scattering and a one-loop correction: ![Compton Scattering][1] $$(-ie)^4\...
2
votes
0answers
130 views

Why do tadpoles contribute to amplitudes?

In some quantum field theories tadpoles of the form                           &...
1
vote
0answers
121 views

Fermion - Antifermion (annihilation) scattering amplitude

I'm trying to get the scattering of the diagrams described here in the "annihilation, part ii" (fermion/antifermion - scalar/scalar) http://www.physics.umd.edu/courses/Phys624/agashe/F10/solutions/HW7....
1
vote
1answer
84 views

Photon emission/absorption by an atom and local gauge invariance

I understand that the local gauge invariance leads to a photon emission/absorption when the phase of an electron field is changed while the amplitude being unchanged. I'd like to know whether this ...
2
votes
1answer
204 views

Particle Physics Decay Question - Eta Prime Decay Parity/Angular Momentum Conservation

I was hoping someone could clarify why the following decay does not occur: $ \eta ^{'0} \rightarrow \pi ^{0} + \rho ^{0}$ The quark compositions and spin parity are as followed: $ \eta ^{'0} : (u\...
0
votes
1answer
42 views

colliding point particles

when I draw e.g. the diagram of compton scattering I assume that the electron of given momentum gets 'hit' by a photon and interacts with it. How close does the photon have to get to the electron that ...
12
votes
4answers
2k views

Do virtual particles actually physically exist?

I have heard virtual particles pop in and out of existence all the time, most notable being the pairs that pop out beside black holes and while one gets pulled away. But wouldn't this actually violate ...
4
votes
1answer
109 views

Magnetic moment in four-fermion theory

I'm trying to calculate the neutrino magnetic moment in the theory with this additional term in the Lagrangian: $\frac{a}{M^2}(\bar{\nu}\sigma_{\mu\nu}\nu)(\bar{e}\sigma^{\mu\nu}e)$, where $\sigma^{\...
1
vote
1answer
80 views

Simple generalization of the Feynman rules for QFT to thermal QFT?

Assuming that one knows Feynman rules for QFT, what is the simplest way to generalize them for $T \neq 0$ case? What is the main difference? Can we just read them off from Lagrangian the same way as ...
1
vote
2answers
107 views

Ambiguity regarding Feynman Diagrams

I recently started learning feynman diagrams but I am a bit confused by how they are constructed from scratch (we are expected to memorize them without knowing exactly how they work). In particular, ...
2
votes
1answer
473 views

Feynman rules for gauge bosons and Goldstone bosons

Does anyone know where I can find: gauge boson propagators (in an unfixed gauge) for the unphysical Electroweak gauge bosons $A^1_\mu$, $A^2_\mu$, $A^3_\mu$ and $A^4_\mu$ whose combinations give the ...
2
votes
1answer
108 views

Scalar Yukawa theory derivation

I am using Tong's notes for QFT, and on page 59 there is a derivation for the scattering amplitude of $\psi\psi \rightarrow \psi\psi$ in Scalar Yukawa theory. It goes from here: $$\langle p_1',p_2'|:...
3
votes
2answers
240 views

Is this symmetry factor in Peskin wrong?

I am trying to compute the symmetry factor of a Feynman diagram in $\phi^4$ but i do not get the result Peskin Claims. This is the diagram I am considering $$\left(\frac{1}{4!}\right)^3\phi(x)\phi(...
1
vote
1answer
151 views

Counting higher-order corrections in “ABC theory”

I am trying to understand how to enumerate higher-order Feynman diagrams. In his book on Elementary Particle Physics, Griffiths considers a simple "ABC toy theory" which has: three (scalar, massive)...
2
votes
1answer
440 views

Why does not Bhabha scattering contain u-channel diagram?

$e^+e^-\rightarrow e^+e^-$ is called Bhabha scattering. Let us only consider the tree level Feynman diagrams of this process. Apparantly, there are s-channel and t-channel diagrams as shown in the ...