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2
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1answer
62 views

How do you prove that $L=I-V+1$ in $\lambda\phi^4$ theory?

It is known that the number of loops in $\lambda\phi^4$ theory is given by the formula $$L=I-V+1$$ where $L$ is the number of loops, $I$ the number of internal lines and $V$ the number of vertices. ...
1
vote
1answer
49 views

First-order EM Feynman diagram?

Is there any 1st order electromagnetic Feynman diagram? I.e. a process whose probability is just $\propto \alpha_{EM}$? If not, is there any physical reason why? We always need at least two particles ...
2
votes
1answer
50 views

Order of Feynman diagrams for electroweak processes?

I want to compare two Feynman diagrams and be able to say which one describes a process that is more likely to happen. As far as I understand, this is done by considering the order of the diagram. ...
2
votes
0answers
125 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 ...
1
vote
2answers
97 views

How to tell the order of a Feynman diagram?

How can we know the order of a Feynman diagram just from the pictorial representation? Is it the number of vertices divided by 2? For example, I know that electnro-positron annihilaiton is first ...
0
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0answers
31 views

Feynman Parametrization in muon magnetic moment

I am calculating the muon magnetic moment due to Electroweak interactions in one loop diagrams involving $W$ bosons. While referring a particular research article by John S. Curiale, titled Weak ...
1
vote
1answer
27 views

Feynman-like diagrams for photon/electron interaction and electron recollision

Feynman diagram is a useful and powerful tool to represent path integrals. But, most of its applications seem to be focused on relativistic particule creation/annihilation. As far as I can ...
1
vote
1answer
100 views

Is there a mistake in a QFT textbook?

I tried to calculate one of the problems in the textbook Gauge Theory of Elementary Particle Physics by Ta-Pei Cheng and Ling-Fong Li. On page 248 you can find the following calculation of a loop ...
3
votes
1answer
43 views

Decay Feynman diagram

$$D^0 \to K^+ +\pi^- + \pi^0 + \pi^0$$ cannot occur by first order weak interactions. Could anybody help me confirm this? What I currently have is that the initial charm goes to anti-strange and the ...
2
votes
0answers
56 views

Calculating imaginary part of a loop diagram using cutting rules for phi^4 theory [closed]

I'm trying to calculate the imaginary part of this diagram in $\phi^4$ theory, using the optical theorem, and I'm having trouble. The cutting rules seem to suggest that this diagram is equal to ...
1
vote
1answer
44 views

Using the optical theorem to calculate the imaginary part of a loop diagram

I'm trying to calculate the imaginary part of this diagram in $\phi^4$ theory, using the optical theorem, and I'm having trouble. All of the examples I can find use the theorem to relate the ...
0
votes
1answer
42 views

Feynman Diagram in QED non relativistic limit

I am following Peskin to read Feynman diagram. But in this image given, he used the non-relativistic limit to write the incoming fermion gamma mu product. How did he get it? Any explanations in ...
2
votes
1answer
55 views

Performing one-loop “triangle” integral

Let's have integral $$ \tag 1 I_{\alpha \beta \gamma \delta} = \int d^{4}qD^{V}_{\alpha \beta}(k + q)D^{V}_{\gamma \delta}(q + k - p)D^{f}(q), $$ where $D^{V}_{\alpha \beta}$ corresponds to massive ...
0
votes
0answers
34 views

What do the tensors here equal to?

In the process $$e^+e^- \rightarrow \gamma \gamma$$ for which the amplitude can be written as: $M= \epsilon^*_{1\nu}\epsilon^*_{2\mu}(A^{\mu\nu}+\tilde{A}^{\mu\nu})$, where $\epsilon_i$ is the ...
4
votes
1answer
93 views

Gauge invariance (QED)

In his book, the author says that according to the Feynman diagrams of this process in QED $$e^+ e^- \rightarrow \gamma \gamma,$$ gauge invariance requires that $$k_{1\nu}(A^{\mu\nu} + ...
1
vote
2answers
162 views

Having Trouble Understanding Feynman Diagrams [closed]

So recently I have became interested in quantum physics. However when I read up on quantum physics Feynman diagrams appear everywhere, and I do not understand them! Here is a Feynman diagram that is ...
1
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0answers
49 views

Shifting the integration variable in loop integrals

We know that, in four dimensions, shifting the integration variables is valid only for convergent and logarithmically divergent integrals. If we employ a hard cutoff $\Lambda$, is it permissible to ...
0
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0answers
30 views

How to calculate explicitly the *external leg correction* diagram

I tried to calculate the Amplitude of the external leg correction of figure 6.1 in Peskin&Schroeder. I focus on the diagram with one incomming charged fermion $f^-$ (with momentum $p'$), then a ...
3
votes
1answer
114 views

Tadpole diagrams in $\phi^3$ theory

In "Quantum Field Theory" by Mark Srednicki, Chapter 9 page 67, after he proves that $\langle 0|\phi(x)|0 \rangle$ vanishes (meaning sum of all connected diagrams with a single source is zero), he ...
1
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0answers
63 views

QFT Perturbative analysis of multiple atom-level quantum computers close to each other

Following up on this question, I'm wondering about electromagnetic interactions perturbation expansions close to a "black-box" quantum computer and modularity of Feynman diagrams in general. Let me ...
0
votes
0answers
35 views

Correction of arrow of particle direction

I have seen a stamp of Richard Feynman where Feynman hold the famous Feynman diagram. But is there any problem of the direction of arrow?
1
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0answers
39 views

Diagrammatics of Slavnov Taylor Identity

Is there a reference other than the original paper of 't-Hooft and Veltman, where I can get a pedagogical introduction to the diagrammatic approach to understanding the BRST-Ward or Slavnov-Taylor ...
1
vote
3answers
105 views

Quark anti-quark pair creation. Do we need a gluon?

What is the difference between these diagrams? Is the presence of the gluon taken for granted in the second one? and EDIT: I just zoomed into the picture, it is not a single quark state. ...
2
votes
1answer
98 views

How do I calculate a Feynman diagram with one loop?

I'm following Peskin & Schroeder and I'm trying to calculate the momentum space representation for the following diagram, Q4 in this link. Paper The loop is what's causing me problems. I'm not ...
3
votes
1answer
95 views

$\mathrm{\rho^0}$ meson decay via the weak interaction?

Of course, the $\mathrm{\rho^0}$ meson can decay in $\mathrm{\pi^{+}\ \pi^{-}}$ through the strong interaction. Using Feynman diagrams, I cannot understand why the same decay couldn't happen through ...
2
votes
2answers
359 views

Feynman paths of FTL velocity have imaginary momentum?

In this answer it is discussed that Feynman path integrals sums amplitudes for all possible paths, including those that are not time-like. If you take the momentum-space path integrals, I would ...
2
votes
0answers
50 views

Off-shell legs in Feynman diagrams

I have a tree-level diagram with one leg being off-shell (its momentum beeing $\mathcal{O}(m_B)$). How do I treat this leg when computing the amplitude? Do I put in the propagator and ignore the ...
1
vote
1answer
61 views

Outside of string theory, can exchange particles be understood as being one-dimensional?

I'm pretty new to quantum, without any formal education therein, so forgive my general layman ignorance when I ask how it is that point-like exchange particles can be modeled in Feynman diagrams as ...
2
votes
1answer
217 views

Mølller scattering

I came across Mølller scattering today (which is just a fancy name for electron-electron scattering. I'm confused as to why there are two tree level Feynman diagrams for this process: Check out the ...
1
vote
0answers
57 views

How to deal with coupled fermion boson operators?

I am a beginner in field theory and I have an exercise where I have a product of coupled fermion boson operators? $$ \hat{b_{l} }^{\dagger}\hat{c_{l^{'}} }^{\dagger}\hat{a_{q} }\hat{b_{l} ...
2
votes
1answer
204 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
2
votes
1answer
75 views

Quick non rogorous way to obtain Feynman rules from a Lagrangian in a non abelian theory

I have been told that a quick way to get the Feynman rules from a Lagrangian is to take an interaction term, forget about the fields and multiply an $i$. This works perfectly for example for QED but I ...
2
votes
1answer
65 views

Can you draw a Feynman diagram for electronic transition between two energy states?

How would you represent this situation using Feynman diagram? Thanks!
3
votes
2answers
118 views

How to calculate the tree-level probability amplitude for the electron-positron to muon-antimuon process?

Consider the following process: $e^+ + e^- \rightarrow \mu^+ + \mu^-$. I'm trying to calculate the probability amplitude of such a process in leading order. In leading order the amplitude is given ...
2
votes
1answer
91 views

Virtual Photon transmission speed of a Static Electric Field?

In the case of a non-accelerating point charge "A" of stable velocity, its static field is treated as though it is instantaneously present at a distance, i.e. a second point charge "B" will react to ...
3
votes
1answer
214 views

Charged current vs. neutral current neutrino interactions

I am doing research related to the detection potential of neutrino detectors and, in looking up the various neutrino interaction channels that exist in each detector, I have found the interactions ...
2
votes
1answer
114 views

Total divergence term and corresponding Feynman Diagram

A total divergence term added to the Lagrangian doesn’t affect the action because the integral of a total divergence vanishes. But if one attempts to derive the Feynman rules from the Lagrangian with ...
1
vote
2answers
192 views

Feynman-Stueckelberg interpretation

My question is related to the interpretation of antiparticles. According to the so called Feynman-Stueckelberg interpretation a negative energy solution of the Dirac equation corresponds to a positron ...
1
vote
1answer
47 views

Representing momentum exchange in Feynman diagrams

I'm a bit confused about how momentum exchange is represented in Feynman diagrams. I'm going through Tongs qft notes on interactions right now and he demonstrates how to draw Feynman diagrams with a ...
1
vote
1answer
132 views

Feynman diagrams for scalar field: which particle are we drawing?

Chapter I.7 of Zee's Quantum Field Theory in a Nutshell is an introduction for Feynman diagrams in the context of a scalar field $\varphi$, with Lagrangian $\mathcal{L} = \frac12[(\partial ...
3
votes
0answers
144 views

How to count and 'see' the symmetry factor of Feynman diagrams?

Could somebody explain how one can derive the symmetry factor both by counting possible contractions and by looking at the symmetry of a diagram. Consider for example this diagram in $\phi^4$-theory ...
1
vote
1answer
39 views

The one-loop contribution to a time ordered product of conserved currents

In two dimensions one can define for a Lagrangian describing free Dirac fermions with $N$ associated flavours by $$\mathcal{L}=i\bar{\psi}_i\gamma^\mu \partial_\mu \psi^i $$ and associate vector ...
2
votes
1answer
53 views

Fast and slow modes, and the vanishing of certain diagrams during re-normalization

In the middle of pg. 452 of Atland and Simonss Condensed Matter Field Theory, they state the following: Terms of $\mathcal{O}(\phi _{\text{s}}^3\phi _{\text{f}})$ do not arise because the addition ...
3
votes
1answer
78 views

Infinitely many scalar fields

Suppose I have the following Lagrangian density: $$ \mathcal L = -\frac{1}{2} \sum_{i = 1}^N \left [ \partial_\mu \phi_i\partial^\mu \phi^i +m^2 \phi_i^2\right ] + \frac{g}{2N}\sum_{i=1}^N ...
1
vote
1answer
130 views

Feynman rule for propagator with derivatives

Suppose you have an interaction term of the form $$\mathcal{L}_{int} = \frac{h g}{3!}\phi^3\partial^2\phi$$ where $h $ and $g$ are both couplings. Now if I draw a diagram of the form given in the ...
3
votes
1answer
142 views

Relationship between the on-shell and BPHZ renormalization schemes

In his book Quantum Field Theory - A Tourist Guide for Mathematicians, Gerald Folland introduces the on-shell renormalization scheme for the $ \phi^{4} $-scalar field theory. According to my ...
1
vote
1answer
58 views

What are Maximally Helicity Violating (MHV) Amplitudes?

Definition of MHV amplitudes on Wikipedia: In theoretical particle physics, maximally helicity violating amplitudes are amplitudes with n external gauge bosons, where n-2 gauge bosons have a ...
1
vote
1answer
180 views

Neutrino-Neutron Interaction Feynman Diagram (W Boson Direction)

I am currently studying differential cross sections for my Nuclear Physics module. I'm looking an experiment where muon-neutrinos are interacting with nucleons in a scintillator producing muons (which ...
1
vote
1answer
90 views

Guidance needed in finding scattering amplitude

If I have the Lagrangian $$\mathcal{L}=\bar{\psi}(i\gamma ^\mu \partial_\mu - m)\psi -g\bar{\psi}i\gamma^5\phi\psi,$$ where $g$ is a coupling constant. How to find the scattering amplitude for $$ ...
1
vote
2answers
66 views

Off-shell external line

In some QFT textbooks, an external line which is off mass shell also concerns us. But according to the motion equation, shouldn't the single external line be on the mass shell? Especially when we ...