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4
votes
1answer
211 views

Symmetry factor for Feynman diagrams in $\phi^4$-theory for $n$-points Green function

I'm working with two theories. Theory A: $H_{int} =\int d^3x \frac{Mg}{2}\phi\varphi^2$ Theory B: $\phi^4$-interaction: $H_{int} = \int d^3 x \frac{\lambda}{4!}\phi(x)^4$ Where $M$ is the mass ...
2
votes
0answers
116 views

Feynman amplitude for electron-positron annihilation and $W^{\pm}$ production

I'm working with this interaction Hamiltonian density $$ H_{int}(x) = ig\bar{\Psi}_{\nu_e}(x)\gamma^\rho P_L \Psi_e(x)V_\rho(x) + igV^\dagger_\rho(x)\bar{\Psi}_e(x)\gamma^\rho P_L \Psi_{\nu_e} $$ ...
0
votes
2answers
94 views

Momentum conservation in the one-loop contribution of the photon propagator

The lowest contribution to the photon self-energy is represented by the following diagram (Taken from F.Schwabl, Advanced quantum mechanics, p.365):: ($k$ is the momentum of the photon that decays in ...
1
vote
0answers
83 views

How does one calculate Feynman rules from a given lagrangian in QED?

I am a beginner in learning QFT. In homework problems in QED I often meet questions that asks one to calculate Feynman rules from some given lagrangian density. Some simple idea is to "read off" the ...
0
votes
1answer
203 views

Why four-point vertex function in $\phi^3$ theory?

So as I understand it the order of $\phi$ in a scalar Quantum field theory is indicative of the number of lines entering a given vertex. For example for $\phi^3$ this leads to vertices like the one ...
1
vote
0answers
64 views

How do I decide when to use raised/lowered indices when calculating the amplitude of a Feynman diagram?

I am learning the Feynman rules for QCD. The book I am reading tells me that gluon propagators contribute a factor of $$\frac{-ig_{\mu\nu}\delta^{\alpha\beta}}{q^2}$$ However, in one of the ...
0
votes
0answers
19 views

derivation of formula for number of closed loops in a Feynman diagram [duplicate]

How does one derive the formula $$V=I-L+1$$ where $V$=No. of vertices, $I$= No. of internal lines and $L$=No. of closed loops. I've seen it stated in several lecture notes on QFT but none (that I ...
0
votes
0answers
36 views

Feynman diagrams with ghosts and symmetry breaking

Let us think of an abelian gauge theory, precisely a scalar QED with 3 complex components of the scalar field and a 4-degree auto-interaction mixing components. Let us consider a spontaneously ...
5
votes
1answer
70 views

Why is the $D^0$ oscillation so different from the $K^0$ and $B^0$?

I have looked for this answer into many articles and books but I am not able to figure out why $D^0\to\bar{D}^0$ is so highly suppressed if compared to the $B^0 \to \bar{B}^0$ and $K^0 \to \bar{K}^0$ ...
3
votes
1answer
422 views

Do we need virtual particles?

I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, ...
3
votes
1answer
115 views

How does order of scalar $\phi$ interaction impact feynman diagrams?

On page 60 of srednicki (72 for online version) for the $\phi^{3}$ interaction for scalar fields he defines $Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta ...
3
votes
1answer
167 views

Tadpole diagram in QED

In $\phi^4$ theory with the $\lambda \phi^4 / 4!$ interaction term gives rise to “tadpole” diagrams like this: If I have a standard QED interaction with $e \bar\psi \gamma^\mu \psi A_\mu$, can I ...
1
vote
0answers
49 views

QFT decay rates in lower dimensions

My starting point is the decay of a Higgs particle into two fermions, with decay rate proportional to \begin{equation} \Gamma \propto g_\psi^2 N m, \end{equation} where $g_\psi$ is the coupling, $N$ ...
2
votes
0answers
128 views

Number of distinct Feynman Diagrams for different orders of $\phi^4$ theory for 2 point function

There is 1 distinct Feynman diagram for zeroth order and 2 distinct diagrams for first order in $\phi^4$ theory for two point function. I want to know is there a way to predict the number of distinct ...
2
votes
0answers
94 views

Is this an error in A.Zee's 《Quantum Field Theory in a Nutshell》?

I am reading A.Zee's 《Quantum Field Theory in a Nutshell》 page 44. He is trying to evaluate $Z(J)=\int_{-\infty}^{+\infty}dq e^{-\frac{1}{2m^{2}}q^{2}-\frac{\lambda}{4!}q^{4}+Jq}$ Of the term ...
0
votes
0answers
136 views

How do I get the amplitude for the one-loop photon self-energy?

I am studying Maggiore's book on QFT and I am stuck in the amplitudes of one-loop corrections in QED. Could someone clearly explain me how do I get the following amplitude from the respective diagram? ...
1
vote
0answers
52 views

Combinatorics of fourth order feynman diagram

I am trying to calculate how many different forth order feynman loop diagrams I can produce. I know that for 2nd order it is 6x3x2 thus 3! since you start with 3 lines coming out of each vertex so 6 ...
0
votes
0answers
61 views

Propagator for fermion fields and Feynman diagrams

I need some help concerning the interpretation of propagators and Feynman diagrams. The free fermion propagator is given by the contraction of two fields $\psi(x),\bar\psi(y)$: ...
3
votes
2answers
153 views

Feynman diagram for attractive forces

I’m looking at Feynman diagrams for attractive forces and I'm thoroughly confused. Below are three diagrams from HyperPhysics: These all illustrate instances where the forces are attractive. ...
0
votes
0answers
140 views

u-Channel Matrix element for electron-positron annihilation

This one is a quantum related question. The calculation relates to the Matrix element for the annhilation of a electron-positron into two photons: $$ e^-e^+\rightarrow\gamma\gamma $$ I've recently ...
0
votes
1answer
121 views

Is a Feynman diagram depicting a vacuum bubble “that gets real” valid?

In exercise I.7.3 of A. Zee's QFT in a Nutshell, we have to draw all the Feynman diagrams of the scalar theory $$ Z(J) = \int D\varphi e^{i\int d^4x\{\frac ...
2
votes
0answers
40 views

Is this the correct way to obtain $<f|i>$ term in $\phi^4$ interaction theory? [closed]

Lets first write the expectation value of the fields in the interaction picture; $$ ...
0
votes
1answer
41 views

What does “n-particle reducible” mean?

I am reading Ramond and in page 112 he says "In $\lambda \phi^{4}$ theory, diagrams can be at most three-particle reducible". My question: whether the individual Feynman Diagrams are treated as ...
0
votes
0answers
23 views

IBP Identities to solve differential equation

I am wondering if anyone has experience in using IBP( Integration by parts) identities in the evaluation of Feynman diagrams via differential equations? My question is that I can't seem to understand ...
0
votes
1answer
85 views

Photon-Photon-scattering (Feynman diagram)

The feynman diagram for the Delbrück-scattering (photon-photon-scattering) in the lowest order looks like as in the picture: But why is the following diagram equal to one of the upper three? There ...
1
vote
1answer
118 views

Zee's Nutshell: Feynman diagrams “baby problem”: Connected vs. Disconnected

On page 47 of A. Zee's QFT in a Nutshell, he explains how disconnected Feynman diagrams can be built from lower-order connected diagrams: I don't know how to understand formula $(6)$. I understand ...
0
votes
0answers
78 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
votes
1answer
107 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
votes
0answers
124 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 ...
0
votes
0answers
70 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
1answer
85 views

How to derive the vertex factor for the four-field interaction in scalar QED?

I tried to find the Feynman rules using path integral. For scalar QED, I have an interaction term $e^2\phi^{\star}A_{\mu}^2\phi$. Generating function then can be written as $$ ...
1
vote
0answers
71 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
224 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
189 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
vote
1answer
104 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
vote
0answers
67 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
91 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 ...
1
vote
1answer
109 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
vote
0answers
70 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
834 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
47 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
115 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
86 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
votes
0answers
79 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, $$ ...
4
votes
2answers
74 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 ...
0
votes
0answers
27 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
47 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
vote
0answers
47 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 ...
2
votes
1answer
135 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 ...
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 ...