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50
votes
2answers
5k views

Why did Feynman's thesis almost work?

A bit of background helps frame this question. The question itself is in the last sentence. For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly ...
22
votes
3answers
923 views

The path integral and Feynman diagrams

This question is somewhat of a historical one, but it also contains some physics. I am curious to find how exactly the concept of Feynman diagrams arose (I assume from Feynman's path integral)? The ...
16
votes
1answer
2k views

Interpretation of derivative interaction term in QFT

I am trying to understand what a term like $$ \mathcal{L}_{int} = (\partial^{\mu}A )^2 B^2 $$ with $A$ and $B$ being scalar fields for instance means. I understand how to draw an interaction term in ...
13
votes
2answers
494 views

Applications of the Feynman-Vernon Influence Functional

I am looking for a reference where the Feynman-Vernon influence functional was defined and used in the context of relativistic quantum field theory. This functional is one method to describe ...
12
votes
3answers
1k views

Feynman diagrams in effective theories

I've been seeing many feynman diagrams lately that I can't quite interpret yet. I've heard a basic Quantum Field Theory lecture and so to me, a Feynman diagram is simply a mnemonic picture to quickly ...
12
votes
1answer
1k views

Software for calculating Feynman Diagrams

Is there a software (open source preferred) where I would input something like "Ingoing: a fermion $(p1, s1)$ and a photon $(p2, s2)$. Output: A fermion $(k1, r1)$ and a photon $(k2, r2)$" and I would ...
11
votes
4answers
7k 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: ...
11
votes
3answers
3k views

Gentle introduction to twistors

When reading about the twistor uprising or trying to follow a corresponding Nima talk, it always annoys me that I have no clue about how twistor space, the twistor formalism, or twistor theory works. ...
11
votes
3answers
441 views

Does radio use virtual photons?

In radio communication each accelerated electron in the transmitter antenna interacts with an electron in the receiver antenna by exchanging a photon. Is that photon always a virtual photon as ...
10
votes
1answer
374 views

Any practical results yet from 'Twistor Uprising'?

In Nima's lectures on the 'Twistor Uprising' (for example here), he gushes about about new powerful techniques for calculating amplitudes, such as summing Feynman diagrams using 'BCFW recursion.' He ...
10
votes
2answers
783 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
9
votes
2answers
375 views

In what sense are loop diagrams quantum corrections?

What's so not-quantum about tree-level diagrams?
9
votes
2answers
397 views

How to prove equivalence of RG flow of QFT coupling constant and diagrammatic resummation at fixed renormalization scale?

QFT books say that solving the RG equation $\frac {dg} {d\textbf{ln} \mu}=\beta(g)$, using the one-loop beta function, is to the "leading log" approximation equivalent to resumming infinitely many ...
9
votes
1answer
425 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 ...
8
votes
3answers
781 views

MVH amplitudes and the unitarity method

In the last 5 years there has been a silent revolution in QFT called the unitarity method and the Maximum Violating Helicity (MVH) Amplitudes that basically consist an alternative way to obtain the ...
8
votes
3answers
290 views

Problem understanding the symmetry factor in a feynman diagram

I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are in $\phi^4$ ...
8
votes
1answer
692 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 ...
8
votes
3answers
2k views

Recipe for computing vertex factors in Feynman diagrams

I am currently studying quantum field theory from Srednicki. In class we have covered till chapter 14 and then skipped to IR divergences. So my knowledge of quantum field theory is limited to those ...
8
votes
2answers
298 views

Tadpole symmetry factor

Can someone help me with symmetry factor of one-loop tadpole diagram (one loop correction to one point Green function in phi-3 theory)?
8
votes
1answer
553 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 ...
8
votes
1answer
408 views

Coleman-Weinberg potential: resum at 2 loops?

Say we want to compute the Coleman-Weinberg potential at 2 loops. The general strategy as we know is to expand the field $\phi$ around some background classical field $\phi \rightarrow \phi_b + ...
7
votes
3answers
780 views

What makes a Feynman diagram real or virtual?

Simple question: as the title says, what makes a real Feynman diagram real, and what makes a virtual diagram virtual? Or in other words, how do I tell whether any given diagram is real or virtual? ...
7
votes
3answers
3k views

Electron Positron annihilation Feynman Diagram

I am having some trouble understanding this fenyman diagram, it seems to indicate that the electron produces the positron, as the arrow of the positron is pointing from the electron. Additionally ...
7
votes
1answer
87 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:
7
votes
0answers
630 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 ...
6
votes
4answers
330 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 ...
6
votes
2answers
69 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 ...
6
votes
3answers
324 views

Is there a simple way to compute some physical constant from Feynman diagram statistics?

I've been playing around writing some software to generate Feynman diagrams for QED, respecting the vertex "rules" described here, and avoiding creating isomorphic duplicates. So from a starter ...
6
votes
2answers
1k views

How do we distinguish between virtual particle exchange and particle decay?

The difference between virtual particles and unstable particles is discussed at length in this question (namely, virtual particles correspond to internal lines in Feynman diagrams and are not ...
6
votes
1answer
248 views

Two-loop regularization

Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral $$ ...
6
votes
2answers
685 views

Feynman rules with helicity states.

Whenever Feynman rules are stated they are always without any mention of the helicities - this I find to be very confusing. How does one introduce and account for that? Is there an intuitive/simple ...
6
votes
1answer
121 views

Why is there no double counting of $s$- and $t$-channels in string theory?

In string theory for the four particle tree diagram exchange, why is there some mysterious crossing duality between the $s$- and $t$- and $u$-channels? Why isn't there a double counting in the Feynman ...
6
votes
1answer
338 views

Can a photon see ghosts?

Does it make sense to introduce Faddeev–Popov ghost fields for abelian gauge field theories? Wikipedia says the coupling term in the Lagrangian "doesn't have any effect", but I don't really know ...
6
votes
2answers
261 views

Feynman Diagrams in 2 component notation

When using two component notation people often prefer to refrain from using arrows in Feynman diagrams to denote charge flow as is done in four-component notation. Instead, if understand correctly, ...
6
votes
1answer
327 views

How to sum over final, and average over initial color states?

Consider the $s$-channel mediated top quark production process $$ d + \overline d \rightarrow t + \overline t$$ Using the Feynman rules for QCD, the amplitude contains a color factor $$[c^\dagger ...
6
votes
1answer
121 views

The process $\mu^+\mu^-\rightarrow hh$

I am doing some calculations in the Standard Model. I have a question that seems rather simple but makes me think a lot. I want to compute the cross section of the following process at the leading ...
6
votes
1answer
595 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
1answer
292 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 ...
6
votes
1answer
276 views

SUSY, ways to boost Chargino/Neutralino production?

Does anybody know a good reference that works out the equations for the Chargino/Neutralino production cross section in SUSY? I'm trying to understand if there are any tricks for boosting the ...
6
votes
3answers
542 views

Can photons have negative energy?

Apparently there are 2 electron self-energy graphs possible. The first, the more "familiar", where the incoming electron at time $t_1$ splits up in a photon and an virtual electron. At $t_2>t_1$ ...
6
votes
0answers
180 views

Deriving Feynman rules from Renormalized Lagrangian

In the context of Renormalized Pertubation Theory Peskin Schröder says: The Lagrangian $$ \mathcal{L}=\frac{1}{2} (\partial_\mu\phi_r)^2-\frac{1}{2}m^2\phi_r^2-\frac{\lambda}{4!}\phi_r^4 + \frac{1}{2} ...
6
votes
0answers
318 views

gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
6
votes
0answers
311 views

An use of the Schwinger-Dyson equation

I was confused as to how the equation 10 on page 7 or equation 21 on page 8 of this paper http://arxiv.org/abs/1211.1866 was derived. Can someone explain from where does this come and what do the ...
5
votes
1answer
467 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 ...
5
votes
1answer
399 views

QED Vertex Factor/Rule

On page 303 in Peskin&Schroeder they give the vertex factor as $$V = -ie\gamma^\mu \int d^4x$$ while on page 304 they write $$V_\times = -ie\gamma^\mu\int d^4x A_\mu(x).$$ Why are the ...
5
votes
1answer
629 views

Why do disconnected diagrams not contribute to the S matrix?

I've read somewhere that disconnected diagrams do not contribute to the S-matrix. I don't see why this is the case. I do know why vacuum bubbles do not contribute: given a generating functional for a ...
5
votes
3answers
327 views

Dimensional Regularization Integral Formula

In the formula $$\int \frac {d^{4-2\epsilon} \ell} {(2\pi)^{4-2\epsilon}} \frac 1 {(\ell^2-\Delta)^2} = \frac i {(4\pi)^{2-\epsilon}} \Gamma(\epsilon) \left(\frac 1 \Delta\right)^\epsilon,$$ how ...
5
votes
1answer
121 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[ ...
5
votes
2answers
623 views

Feynman rules for SUSY

This might be an incredibly naive question, but I'm wondering if there are a set of rules for "translating" between Standard Model and SUSY. For instance, if I want want to go from a Standard Model ...
5
votes
1answer
613 views

A question about Feynman diagram and symmetry factor

Consider a $\varphi^3$ theory: $$ Z_1(J) \propto \exp\left[\frac{i}{6} Z_g g\int \mathrm{d}^4 x \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right] Z_0(J), $$ where $$ Z_0(J) = ...