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2
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1answer
60 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
53 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
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2answers
82 views

Dashed lines in Feynman diagram

In this article, in e.g. figure 2, what does these dashed lines across the Feynman diagram mean?
8
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1answer
279 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 ...
2
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1answer
54 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 ...
8
votes
1answer
346 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 ...
3
votes
3answers
67 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 ...
3
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0answers
79 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: $$ \tag 1 \hat{V}(t) \to \hat{V}(t) + \sum_{a}\int d^{3}\mathbf x \hat{o}_{a}(\mathbf x ,t)\varepsilon_{a}(x). $$ ...
4
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1answer
337 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 ...
1
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0answers
29 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 ...
1
vote
1answer
261 views

Superficial Degree of Divergence for Feynman Diagrams

The superficial degree of divergence for a diagram is defined as the power of $k$ in the nominator minus the power of $k$ in the denominator. It is written to be equal to $4\times$ ...
1
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3answers
86 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
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0answers
24 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
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0answers
52 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
172 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 + ...
4
votes
1answer
210 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
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0answers
77 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
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0answers
45 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: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$ ...
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0answers
26 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 ...
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0answers
26 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
56 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
81 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
254 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 $t_2>t_1$ ...
3
votes
2answers
332 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 ...
6
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0answers
94 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} ...
3
votes
0answers
56 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 ...
17
votes
3answers
580 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 ...
4
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0answers
43 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
1
vote
1answer
58 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
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0answers
29 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 ...
2
votes
0answers
65 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
48 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
123 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 $O(\lambda^2).$ ...
2
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0answers
66 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
151 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
180 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) = ...
0
votes
1answer
250 views

Does path integral and loop integral in a Feynman diagram violate special relativity?

Consider a correlation function between two points $A(x_1,t_1)$ and $B(x_2,t_2)$, we need to integrate over paths which could be infinite long. But the time length $(t_1-t_2)$ is finite, so if $A$ ...
3
votes
1answer
334 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?
3
votes
1answer
71 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 ...
1
vote
1answer
123 views

How to prove useful property of logarithm of generating functional in QFT?

How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.
-2
votes
3answers
188 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
340 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
1answer
53 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 ...
4
votes
1answer
267 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 ...
2
votes
0answers
46 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
120 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 ...
3
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0answers
59 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: ...
5
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0answers
103 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 ...
2
votes
1answer
243 views

Feynman propagators for scalar fields

If there are few massless scalar field, are the propagators of those different massless scalar fields indistinguishable?
3
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0answers
99 views

Why do we use functional integration in QFT?

Recently I learned functional integral's formalism in QFT. I have realized that I don't understand why exactly do we introduce it. We have the expression for $S$-matrix, then we may rewrite it in ...