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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 ...
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1answer
40 views

Peskin “An Introduction to quantum field theory”, problem 4.1 [on hold]

I'm trying to solve problem 4.1)c) in Peskin's book "An Introduction to quantum field theory" using this answer sheet. I don't understand why lambda correspond to a line in Feynman diagrams. Any idea? ...
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1answer
61 views

Integral calculation [on hold]

I do some calculation in QED, but I can not calculate such integral $$ I(a_1,a_2,m_1,m_2)=\int\frac{ d^2\mathbf{x} d^2\mathbf{y}}{(1+\mathbf{x}^2)(1+\mathbf{y}^2)((\mathbf{x}+a_1 ...
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0answers
22 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 ...
2
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0answers
116 views

How do I do this loop integral? [migrated]

I'm having some trouble doing a loop integral. It is the loop integral that gives neutrinos their mass in the famous Zee model (http://dx.doi.org/10.1016/0370-2693(80)90349-4). The integral is $$ ...
3
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1answer
87 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 ...
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0answers
57 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
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0answers
34 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?
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0answers
32 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
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3answers
87 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
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0answers
62 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
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1answer
62 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
345 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
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0answers
46 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
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1answer
55 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
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1answer
204 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
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0answers
50 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
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1answer
83 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
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1answer
59 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
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1answer
54 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
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2answers
101 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
82 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
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1answer
104 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
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1answer
103 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 ...
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2answers
143 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
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1answer
36 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
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1answer
110 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
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0answers
123 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
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1answer
37 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
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1answer
52 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
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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
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1answer
103 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
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1answer
112 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 ...
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1answer
50 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 ...
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1answer
133 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
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1answer
86 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 $$ ...
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2answers
63 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 ...
2
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1answer
63 views

Fermion propagator decomposition

I've seen the following decomposition for the fermion propagator for a fermion with momenta $p-k$, and where both $p-k$ and $p$ have a mass of $m$: $$\frac{(\not p-\not k)+m}{(p-k)^2-m^2}\gamma_\mu= ...
4
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1answer
73 views

Is the decay $B\rightarrow K^* \gamma$ decay allowed in the Standard Model?

This is my idea of the Feynman diagram of the $B^0$ to a $K^0$ decay: The photon is radiated off by one of the particles, and by $up$ quarks I just mean ($u$,$c$ and $t$) and their antiquarks. how ...
4
votes
1answer
101 views

Non-Perturbative feynman diagrams?

The wikipedia page for Feynman Diagrams claims that Thinking of Feynman diagrams as a perturbation series, nonperturbative effects like tunneling do not show up, because any effect that goes to ...
2
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0answers
96 views

Feynman propagator with general $\xi$ parameter

Hey from my notes in my PS book it seems I have solved this some time in the past, but I cannot seem to get the indices straight this time around. So in deriving the Feynman photon-propagator which ...
3
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1answer
177 views

How are Feynman rules derived (in general)?

There are some questions (not all answered) on how Feynman rules for specific cases are derived (e.g. Sign of Feynman rules with derivative couplings, Feynman rules for coupled systems, How can we ...
1
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1answer
143 views

Relative Minus signs from different Feynman Diagrams

I have a problem understanding the occurrence of a the relative minus signs between contributions, coming from different Feynman diagrams, involving fermions. A simple example is Bhabha scattering ...
1
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1answer
61 views

Evaluating Feynman diagram for coupling between scalar field and dirac particle and anti particle [closed]

If I have a scalar field $\alpha$ and a Dirac particle $\beta$ and its anti particle $\overline{\beta}$, such that the three couple to give a vertex factor of $-ik$ when evaluating the Feynman diagram ...
4
votes
1answer
121 views

Computing box diagrams with non-vanishing external momenta

I'm trying to explicitly compute the following box diagram in the Feynman-t'Hooft gauge: If I neglect the impulsion of the $s$ quark, then the final amplitude is given by $$\mathcal{A} \propto ...
1
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0answers
74 views

How to derive scattering amplitude for scalar particle interaction [closed]

I want to derive the amplitude by feynman rules, the question is below but I don't know how to reach the answer: a spin 0 particle with mass m0 that couples to spin 0 particles with masses m1, . . ., ...
2
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1answer
141 views

About the Feynman parameterization--when the 'Delta' in the denominator is minus, how should I do?

I have thought about this question for a very long time. The question will be described as the following. I have an effective Feynman loop diagram to calculate, which describing B meson decay into 3 ...
3
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1answer
152 views

Graph Theory and Feynman Integrals

In Vladimir A. Smirnov's book Analytic Tools for Feynman Integrals, Section 2.3, the alpha representation of general Feynman integral takes the form $$ F_{\Gamma}(q_1,\ldots,q_n;d) = ...
3
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1answer
205 views

Is there a way to calculate the photoelectric effect in QED via a Feynman diagram?

The photoelectric effect is the historic origin of the quantum particle description of light. From it we learn that when light is shone onto a metal single photons interact with single electrons in ...
5
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1answer
119 views

Variational derivatives of strongly connected diagrams functional in gauge theory

Background In Jorge C. Romao's "Advanced Quantum Field Theory", at the end of page 218, Eq (6.266) reads: $$\tag{1} \left.\frac{\delta^{2}}{\delta \omega^{b}(y)\delta A_{\mu}^{c}(z)}\left[ ...