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2
votes
1answer
43 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
votes
1answer
60 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
74 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 ...
1
vote
0answers
44 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
votes
1answer
114 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
vote
1answer
83 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
vote
1answer
37 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 ...
3
votes
0answers
86 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
vote
0answers
36 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
votes
1answer
108 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
votes
1answer
111 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) = ...
6
votes
1answer
109 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[ ...
2
votes
1answer
63 views

What are the quantum numbers of an exchange particle in the t channel?

i know that for an s channel reaction, the quantum numbers of the intermediate particle have to be the same as those of the particles coming in, for example in the reaction $\gamma \pi \rightarrow a_2 ...
2
votes
2answers
94 views

Dashed lines in Feynman diagram

In this article, in e.g. figure 2, what does these dashed lines across the Feynman diagram mean?
2
votes
1answer
101 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 ...
3
votes
3answers
83 views

How does a photon “know” that it's left one charge and that it's going to another one?

How does it know the same charge it left will be the same charge it will return to? My understanding is photons are neutral and have no charge. i.e. Like charges repel, unlike attract. All charged ...
1
vote
0answers
36 views

Why only fully connected diagrams contribute to T matrix

In Peskin's introduction to QFT, he wrote: only fully connected diagrams, in which all external lines are connected to each other, contribute to the T matrix. I don't understand this ...
3
votes
0answers
87 views

Variations of S-matrix functional and Feynman diagrams in Weinberg QFT

Weinberg on p. 287 of his QFT vol. 1 introduces the extended interaction operator: $$ \tag 1 \hat{V}(t) \to \hat{V}(t) + \sum_{a}\int d^{3}\mathbf x \hat{o}_{a}(\mathbf x ,t)\varepsilon_{a}(x). $$ ...
1
vote
3answers
95 views

Proof of Connected Diagrams

If $Z[J]$ is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $$W[J]\equiv\frac{\hbar}{i}\log\left(Z[J]\right)$$ "generates" only ...
1
vote
0answers
35 views

The Ward identity for EM amplitude with massive vector boson

Let's have theory of massive vector boson interacting with EM field: $$ L = |D_{\mu}W_{\nu} - D_{\nu}W_{\mu}|^{2} + m^{2}|W|^{2}, \quad D_{\mu} = \partial_{\mu} - ieA_{\mu}. $$ The question: how to ...
2
votes
0answers
60 views

S-Matrix Generating Functional (Problem 4.1 in Weinberg)

I'm currently working through Weinberg's QFT book, but I'm somewhat stuck at problem 4.1, which states: Define generating functionals for the S-matrix and its connected part: \begin{equation} ...
7
votes
1answer
197 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 + ...
3
votes
0answers
85 views

Topologically distinct Feynman diagrams

Are these two diagrams topologically distinct? I consider $\phi^4$ theory and use MS-scheme. A vertex corresponding to counterterm $-\imath \frac{m^2 \lambda}{32 \pi^2 \epsilon}$ is denoted by ...
3
votes
0answers
51 views

What is the phase space for outgoing photons?

For a scattering process for which $n$ fermions are scattered, (by some conventions) the cross section acquires a phase space factor of: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$ ...
1
vote
0answers
37 views

Sign of Feynman rules with derivative couplings

Feynman rules for derivative couplings always make me confused. For example, the derivative in $gV^\mu\phi^+\partial_\mu\phi^-$ will give you $\pm ip_{-\mu}$, where $\pm$ depends on whether the ...
1
vote
0answers
30 views

Physical interpretation of scalar tadpole loops

In Feynman diagrams, fermionic loops are drawn like this: While scalar loops are drawn as tadpoles: I assume the difference comes from the scalar not having an anti-particle. But how should one ...
1
vote
1answer
71 views

Symmetry factor of $n$-point one-loop diagram [duplicate]

If we have a one-loop diagram in $\phi ^ 3$ scalar field theory with $n$ external lines, then what is its symmetry factor? I have drawn the diagram I am looking for, but instead of $6$ external ...
3
votes
1answer
96 views

Symmetry factor of Feynman diagram

What is the symmetry factor for the following Feynman diagram if we assume that the external points are held fixed? Please ignore the arrows in the diagram. I am referring to the second diagram on ...
6
votes
3answers
290 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
106 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} ...
4
votes
0answers
51 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
1
vote
1answer
78 views

What is the leading order Feynman diagram for nucleon-anti-nucleon annihilation into two mesons ($\psi^{\dagger} \psi \to \phi\phi$)?

I am working with a standard basic scalar Yukawa theory. I.e. the only interaction term is $-g\psi^\dagger\psi\phi$, where the $\phi$ field quanta are the mesons, the $\psi$ field quanta are the ...
1
vote
0answers
30 views

Estimation of polarization perturbative term

I'm studying a diagrammatic approach to degenerate electron gas. Now I need to prove that the energy contribution, with an arbitrary potential, of polarization at first perturbative order given by the ...
19
votes
3answers
652 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 ...
2
votes
0answers
75 views

Feynman's $i \epsilon$ prescription in loop expansion

I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity? And third, Dyson ...
0
votes
0answers
67 views

Feynman Rules in Momentum space

What's the difference between Feynman rules in momentum space for $\phi^3$ theory and for $\phi^4$ theory? I know it's only a slight difference and perhaps found in the vertex factor? But for some ...
1
vote
1answer
208 views

Feynman Diagram in $\phi^3$ theory

I'm slightly befuddled by is what it means when I'm asked to Draw the Feynman diagram in momentum space for the two point function of $\frac{\lambda}{3!}\phi^3$ theory for order $O(\lambda^2).$ ...
3
votes
0answers
72 views

Symmetry factor of tree diagram

In Mark Srednicki's Quantum field theory(page 89) it says This is a general result for tree diagrams (those with no closed loops): once the sources have been stripped off and the endpoints ...
2
votes
0answers
78 views

Feynman rules of a theory in non-standard form

I am currently studying lecture notes by Akhmedov on interacting scalar field theory in de Sitter space. In these notes, he considers a scalar field theory of the form ...
2
votes
3answers
255 views

What's the difference between t-channel and s-channel in particle physics

As the Feynman diagram shows above. Does the s-channel and t-channel stands for exactly same reaction or they have big difference? Many thanks in advance enter image description here
5
votes
1answer
278 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) = ...
3
votes
1answer
77 views

Is there a way to compute (trivalent) Feynman integrals inductively from smaller diagrams?

Suppose that I would like to compute the Feynman integral associated to the trivalent graph One can argue that this diagram comes from two copies of the smaller diagram glued together at the ...
3
votes
2answers
363 views

Higgs boson production via positron-electron collision

One of the suggested diagrams for the Higgs production is the following: so basically an electron-positron pair annihilates and forms an (excited?) Z boson, which then decays into another (less ...
-2
votes
3answers
219 views

What is the difference between these two Feynman diagrams?

In which direction is time flowing and what reactions do they represent? EDIT for Gigi (I could not add a comment to your answer): 1) Do Feynman diagrams by definition only show fundamental ...
1
vote
1answer
372 views

Feynman diagram for annihilation

What is the difference between these two Feynman diagrams? They should both describe the same physical process, annihilation between an electron and a positron.
2
votes
0answers
53 views

Approximation of skeleton diagrams

I'm studying the diagrammatics for a Bose system (in the superfluid phase) developed by Gavoret and Nozieres (Annals of Physics 28 349 (1964)). In this paper, they show how to solve the problem using ...
5
votes
1answer
131 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 ...
2
votes
1answer
55 views

All angle dependence in $\mathrm{d}LIPS_2$?

Recall that $\mathrm{d}LIPS_2$ (one particle decaying into two particles of the same mass) is given by $$\mathrm{d}LIPS_2 = \frac{\vert{\bf k_1'}\vert}{16\pi^2\sqrt{s}}\mathrm{d}\Omega_{cm}.$$ In a ...
5
votes
0answers
113 views

Functional integral aproach for Feynman rules

I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or ...
3
votes
0answers
64 views

Feynman Toy Model Constraints on Number of Each Kind of External Lines

(From my homework) In our toy model we have three kinds of spinless particles: $A$, $B$, and $C$. The primitive vertex of decay/interaction is shown below: My actual problem statement says: ...