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4
votes
2answers
237 views

$2\pi$ and Feynman Rules

I notice a $2\pi$ term in the $\delta$-function when trying to construct an amplitude using the Feynman Rules. The $2\pi$ also appears as an integration measure to enforce normalisation in the phase ...
8
votes
1answer
683 views

How can we derive the Feynman rule for the ordinary QED 3-vertex?

I have checked some Quantum Field Theory texts that include basic QED and they all include the Feynman rule that each vertex bring with it a factor of $$\pm i e \gamma^\mu$$ but I have yet to find a ...
2
votes
1answer
322 views

Feynman propagators for scalar fields

If there are few massless scalar field, are the propagators of those different massless scalar fields indistinguishable?
8
votes
1answer
548 views

Where does the divergence in the $g\phi^3$ $d=4$ 3 point one loop diagram (three external legs) come from?

$g\phi^3$ , $d=4$ , 3 point One loop diagram (three external legs) Divergence I am trying to find where the divergence factor/pole is on the following diagram in 4 dimensions so that I can use ...
5
votes
1answer
453 views

Connected and strongly connected Feynman diagrams

Recently I read, that only connected Feynman diagrams give contribution of nonzero values into the scattering amplitude. Why it is so and what is the physical sense of connected diagrams (due to ...
4
votes
1answer
215 views

Feynman rule for deriative interaction: an example

Consider a theory for a finite number of real scalar fields $\phi _i$ with interaction terms of the form $$ -\lambda _{ijk}\phi _i\partial _\mu \phi _j\partial ^\mu \phi _k, $$ with the sum over ...
3
votes
0answers
49 views

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 ...
6
votes
0answers
310 views

gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
1
vote
1answer
88 views

Allowed interactions for the neutral weak vector boson

Just wanted to double check a couple of things for my own sanity! I am looking at scattering amplitudes for 2 partons going to two partons with the emission of a Z boson (eventually decaying to e+ ...
5
votes
0answers
156 views

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 ...
0
votes
1answer
137 views

Why do arrows point backwards in time for Feynman Diagrams?

I've been looking into Feynman Diagram for quite some time, and the fact that anti-particles point backwards in time after an interaction has been puzzling me. I understand this to be some convention ...
0
votes
1answer
354 views

If time travel to the past is not possible why is this situation considered in Feynman diagrams?

I recently read R.P Feynman's QED:A Strange Theory of Light and Matter. It is believed that time travel to the past is not possible. Then why is particles going backward in time considered in the book ...
2
votes
1answer
228 views

Feynman diagrams for interacting theory of scalar field

Is it correct that the number of lines originating from vertices on Feynman diagrams is equal to the order of phi in interaction lagrangian for scalar field?
2
votes
1answer
285 views

Why does the counterterm's propagator have inverse units of the propagator? $\phi^4$-theory

According to Peskin & Schroeder (page 325), the Feynman rule for the counterterm ------(x)----- for $$ \frac12 ...
1
vote
2answers
221 views

Feynman Diagrams: Mass Conservation

Can a Feynman diagram end with more matter than it began with? The answer should be no because it would break the law of conservation of mass, right? Example: I learned that two up-quarks could ...
2
votes
0answers
145 views

Møller scattering: twisted?

I am studying the Møller scattering, but I don't know how to get the twisted diagram from the S-matrix. Has anybody a good explanation?
6
votes
1answer
588 views

Scattering amplitude and LSZ formula

I'm arriving at a contradiction. To calculate the scattering amplitude, one usually follows the prescription given by the Feynman rules that you only consider fully connected diagrams with the ...
6
votes
0answers
613 views

If Renormalization Scale is Arbitrary, Why Do We Care about Running Couplings?

For the bounty please verify the following reasoning [copied from comment below] Ah right, so the idea is that overall observable quantities must be independent of the renormalization scale. But at ...
2
votes
1answer
361 views

Scalar two loop diagram in $\varphi^4$ theory

Could someone explain how, or at least show me a link that explicitly shows the calculation of a two-loop corrections to scalar’s two-point function in $\varphi^4$ theory in the massless limit.
3
votes
1answer
322 views

Minus Sign in Feynman Diagram

I've been reading these notes and I can't figure out the why on P.120, it is said that The fermionic statistics mean that the first diagram has an extra minus sign relative to the ψψ scattering ...
1
vote
0answers
98 views

Two forms of Feynman Diagrams?

I am confused. I know Feynman Diagrams looks like the ones here. But then I saw these, look in page 17[1247] of this paper. Any idea?
3
votes
1answer
338 views

Electron-Positron Scattering using the Feynman Rules - Integration Q

I'm doing independent studies on electron-positron scattering, specifically the annihilation diagram contribution to the M matrix in Bhabha scattering, and this is the equation I recovered with the ...
0
votes
1answer
270 views

How to verify gauge invariance of an amplitude

I have calculated a tree level amplitude for Compton scattering (${e\left(p\right)+\gamma\left(k\right)\to e\left(p\prime\right)+\gamma\left(k\prime\right)}$): $${ ...
0
votes
0answers
100 views

Reduced graphs and pinch-singular surfaces

I am reading a book on perturbative QCD by John Collins. In Chapter 5, the terms reduced graph and pinch-singular surface are used for the analysis of mass singularities. However, their meanings are ...
3
votes
1answer
465 views

Evaluation of QED amplitude with 1 external photon

I'm trying to compute the exact QED amplitude with one external photon. Suppose that the photon has 4-momentum $q$ and polarization $\varepsilon^\mu$. Peskin and Schroeder (p318) claim that ignoring ...
1
vote
1answer
512 views

Symmetry factor of a second order four point function term of the $\phi^4$ theory

I am reading Cheng and Li. On page 9, it is written that the coefficient $\frac{1}{2 \cdot (4!)^2}$ for the second order term of the four point function becomes just $\frac{1}{2}$ for the following ...
1
vote
0answers
271 views

Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...
1
vote
0answers
89 views

Exact summation of a sub-class of diagram: do we know the exact solved problem?

In quantum field theories (to be relativistic, (non-)relativistic statistical or whatever), we have the powerful diagrammatic approach at our disposal. Most of the time we can not sum up all the ...
2
votes
1answer
240 views

Vacuum polarization in QCD and gluon bubbles

In analogy to QED, the following Feynman diagram is a diagram contributing to the vacuum polarization effect, leading to anti-screening, asymptotic freedom and running of the strong coupling constant. ...
2
votes
1answer
354 views

What does this feynman diagram represent?

This feynman diagram represents the elastic proton scattering of electrons. The $e^-$ has an initial momentum $k$ and a final $k^\prime$. The circle represents that the target(the proton that is) ...
2
votes
1answer
273 views

Feynman diagram for $\overline{K}\,\!^0$ antimeson production on the quark-level

I've recently stumbled upon a physics problem concerning $\overline{K}\,\!^0$ antimeson production. In this particular example, colliding a $\pi^-$ meson with a stationary proton yields a $K^0$ meson ...
3
votes
1answer
806 views

Formula for Symmetry Factor

In $\phi^3$ theory, are there any formula for determining the Symmetry factor as that is found for the $\phi^4$ theory in any standard book of Quantum Field Theory?
4
votes
1answer
231 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 ...
3
votes
1answer
527 views

Most general Feynman diagram

What is the most general Feynman diagram? Srednicki, in his QFT book, says: The most general diagram consists of a product of several connected diagrams. Let $C_I$ stand for a particular connected ...
4
votes
0answers
64 views

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 ...
3
votes
1answer
310 views

Deriving Feynman Rules (with the presence of a gluon field strength tensor)

If I have a Lagrangian of the form: $$ \mathcal{L} = k \bar{\psi} \varepsilon^{\mu \nu} \lambda^a \phi G^a_{\mu \nu} + h.c. $$ [where $\phi, \psi$ are fermions, $\lambda^a$ are Gellmann matrices, ...
3
votes
1answer
197 views

Four-gauge-boson vertex in non-Abelian gauge theories

In Peskin & Schroeder's book page 524, the following diagram is calculated for the gauge boson self-energy in order $g^2$: In dimensional regularization, its contribution is given by ...
1
vote
1answer
348 views

What are the rainbow and ladder approximations in a solid state physics context?

All references I find talk about quarks and gluons, where I have only very limited knowledge about. From it's name (rainbow) I guess it applies to fermions coupled to bosons and we're interested in ...
1
vote
1answer
1k views

Degree of divergence of a Feynman diagram

I am studying the degrees of divergence of Feynman diagrams. I feel that I miss something but I don't really understand what. Please apologize if this question is silly. Anyway. As an introduction to ...
4
votes
3answers
1k views

Is “Witten's Dog” from a Futurama episode an actual physics concept? [closed]

In an old episode ("Mars University") of Futurama which is a TV show, a character named Professor Farnsworth was trying to lecture "Superdupersymmetric String Theory" and "Witten's Dog" to some ...
3
votes
1answer
332 views

Getting rid of double delta function in Feynman rules

[1] A very simple example of feynman rule for scalar fields. After computing the diagram i have got the following: $$ -i(2\pi)^4g^2\int d^4q \frac{i}{q^2 -m^2c^2}\delta^{(4)}(p_1 - p_3 -q) ...
4
votes
1answer
950 views

One-loop $\phi^4$ theory in $d = 3$

I'm trying to calculate the 1 loop correction to the propagator in massless $\phi^4$ theory, in $d = 3$, just for fun. The diagram just looks like a straight line with a circle touching tangently to ...
6
votes
1answer
286 views

Quantum Electrodynamics

I was wondering if anyone could give a simple explanation of how light interacts with matter. From what I have read in QED, electrons will repel each other because of their ability to emit and ...
3
votes
0answers
121 views

exercise books for Feynman diagrams [duplicate]

I know QFT at graduate level but I'll like to master the skill of working with Feynman diagrams. I'm looking for a book of solved exercises on this topic. Specifically, I'm looking for the kind of ...
1
vote
0answers
131 views

Feynman Diagram for Interaction of Deuteron with Oxygen-16

I have to draw a Feynman diagram for the interaction of a deuteron with Oxygen-16. The interaction is as follows: $ d + {}^{16}O \rightarrow p + {}^{17}O . $ I am generally ok with Feynman ...
2
votes
2answers
367 views

Feynman diagrams in three dimensions

Is there such a thing as an extension of Feynman diagrams into three dimensions? Canonical Feynman diagrams use one space and one time dimension to visualize processes involving elementary particles ...
1
vote
1answer
207 views

Two-photon scattering: colours

Is there a particular conservation principle that necessitates that the outcoming photon pair has the same frequencies as the incoming photon pair? I'm thinking in particular of these Feynman-like ...
11
votes
4answers
6k views

What would the collision of two photons look like?

Could someone explain to me what the collision of two photons would look like? Will they behave like, Electromagnetic waves: they will interfere with each other and keep their wave nature Particles: ...
9
votes
1answer
423 views

How fat is Feynman’s photon?

According to my calculations, it is a lot skinnier than Airy’s photon, but still a whole lot fatter than a straight line. So, how does a photon get from point A to Point B? The ray optics ...
3
votes
1answer
365 views

Wick Rotation, interpretation of $\bar{p}^2$ vs the usual $p^2=m^2$

Suppose we use the metric $(+,-,-,-)$ thus the momentum squared is $p^2 = p_0^2-\vec{p}^2 = m^2>0$ Defining $p_E:=\mathrm{i}\cdot p_0$ and $\bar{p}:=(\,p_E,\vec{p})$ with Euclidean norm ...